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Quadratic Equation Solver

This tool solves quadratic equations and provides step-by-step solutions. It supports equations with both whole numbers and fractions. Get accurate solutions quickly!

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Quadratic Equation Solver

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  1. x = ± 4=±2  EXAMPLE 1 Solve quadratic equations Solve the equation. a. 2x2 = 8 SOLUTION a.2x2 = 8 Write original equation. Divide each side by 2. x2 = 4 Take square roots of each side. Simplify. The solutions are–2and2. ANSWER

  2. ANSWER The solution is 0. EXAMPLE 1 Solve quadratic equations b.m2 – 18 = – 18 Write original equation. m2 =0 Add 18 to each side. m=0 The square root of 0 is 0.

  3. ANSWER Negative real numbers do not have real square roots. So, there is no solution. EXAMPLE 1 Solve quadratic equations c.b2+12=5 Write original equation. b2 = – 7 Subtract 12 from each side.

  4. 9 3 9 z2 = 4 2 4  z = ± z = ± EXAMPLE 2 Take square roots of a fraction Solve 4z2 = 9. SOLUTION 4z2 = 9 Write original equation. Divide each side by 4. Take square roots of each side. Simplify.

  5. The solutions are – and 3 3 2 2 EXAMPLE 2 Take square roots of a fraction ANSWER

  6. 6 x = ± EXAMPLE 3 Approximate solutions of a quadratic equation Solve 3x2–11=7. Round the solutions to the nearest hundredth. SOLUTION 3x2–11=7 Write original equation. 3x2 = 18 Add 11 to each side. x2 = 6 Divide each side by 3. Take square roots of each side.

  7. x± 2.45 ANSWER The solutions are about –2.45 and about 2.45. EXAMPLE 3 Approximate solutions of a quadratic equation Use a calculator. Round to the nearest hundredth.

  8. no solution ANSWER ANSWER ANSWER –5, 5. 0 EXAMPLE 1 for Examples 1,2 and 3 Solve quadratic equations GUIDED PRACTICE Solve the equation. 1.c2 – 25 = 0 2. 5w2 + 12 = – 8 3. 2x2 + 11 = 11

  9. no solution ANSWER ANSWER – , 4 4 10 10 ANSWER – 5 5 , 3 3 EXAMPLE 1 for Examples 1,2 and 3 Solve quadratic equations GUIDED PRACTICE Solve the equation. 4. 25x2 = 16 5. 9m2 = 100 6. 49b2 +64 = 0

  10. – 3.16, 3.16 – 0.58, 0.58 – 2.12, 2.12 ANSWER ANSWER ANSWER EXAMPLE 1 for Examples 1,2 and 3 Solve quadratic equations GUIDED PRACTICE Solve the equation. Round the solutions to the nearest hundredth. 7. x2 +4 = 14 8. 3k2 –1 = 0 9. 2p2 –7 = 2

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