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Simplifying 7.32x2 + 2.82x = 5.51 Reorder the terms: 2.82x + 7.32x2 = 5.51 Solving 2.82x + 7.32x2 = 5.51 Solving for variable 'x'. Reorder the terms: -5.51 + 2.82x + 7.32x2 = 5.51 + -5.51 Combine like terms: 5.51 + -5.51 = 0.00 -5.51 + 2.82x + 7.32x2 = 0.00 Begin completing the square. Divide all terms by 7.32 the coefficient of the squared term: Divide each side by '7.32'. -0.7527322404 + 0.3852459016x + x2 = 0 Move the constant term to the right: Add '0.7527322404' to each side of the equation. -0.7527322404 + 0.3852459016x + 0.7527322404 + x2 = 0 + 0.7527322404 Reorder the terms: -0.7527322404 + 0.7527322404 + 0.3852459016x + x2 = 0 + 0.7527322404 Combine like terms: -0.7527322404 + 0.7527322404 = 0.0000000000 0.0000000000 + 0.3852459016x + x2 = 0 + 0.7527322404 0.3852459016x + x2 = 0 + 0.7527322404 Combine like terms: 0 + 0.7527322404 = 0.7527322404 0.3852459016x + x2 = 0.7527322404 The x term is 0.3852459016x. Take half its coefficient (0.1926229508). Square it (0.03710360117) and add it to both sides. Add '0.03710360117' to each side of the equation. 0.3852459016x + 0.03710360117 + x2 = 0.7527322404 + 0.03710360117 Reorder the terms: 0.03710360117 + 0.3852459016x + x2 = 0.7527322404 + 0.03710360117 Combine like terms: 0.7527322404 + 0.03710360117 = 0.78983584157 0.03710360117 + 0.3852459016x + x2 = 0.78983584157 Factor a perfect square on the left side: (x + 0.1926229508)(x + 0.1926229508) = 0.78983584157 Calculate the square root of the right side: 0.888727091 Break this problem into two subproblems by setting (x + 0.1926229508) equal to 0.888727091 and -0.888727091.Subproblem 1
x + 0.1926229508 = 0.888727091 Simplifying x + 0.1926229508 = 0.888727091 Reorder the terms: 0.1926229508 + x = 0.888727091 Solving 0.1926229508 + x = 0.888727091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1926229508' to each side of the equation. 0.1926229508 + -0.1926229508 + x = 0.888727091 + -0.1926229508 Combine like terms: 0.1926229508 + -0.1926229508 = 0.0000000000 0.0000000000 + x = 0.888727091 + -0.1926229508 x = 0.888727091 + -0.1926229508 Combine like terms: 0.888727091 + -0.1926229508 = 0.6961041402 x = 0.6961041402 Simplifying x = 0.6961041402Subproblem 2
x + 0.1926229508 = -0.888727091 Simplifying x + 0.1926229508 = -0.888727091 Reorder the terms: 0.1926229508 + x = -0.888727091 Solving 0.1926229508 + x = -0.888727091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1926229508' to each side of the equation. 0.1926229508 + -0.1926229508 + x = -0.888727091 + -0.1926229508 Combine like terms: 0.1926229508 + -0.1926229508 = 0.0000000000 0.0000000000 + x = -0.888727091 + -0.1926229508 x = -0.888727091 + -0.1926229508 Combine like terms: -0.888727091 + -0.1926229508 = -1.0813500418 x = -1.0813500418 Simplifying x = -1.0813500418Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6961041402, -1.0813500418}
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