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Simplifying 0 = 0.00787x2 + -1.528x + 72.89 Reorder the terms: 0 = 72.89 + -1.528x + 0.00787x2 Solving 0 = 72.89 + -1.528x + 0.00787x2 Solving for variable 'x'. Combine like terms: 0 + -72.89 = -72.89 -72.89 + 1.528x + -0.00787x2 = 72.89 + -1.528x + 0.00787x2 + -72.89 + 1.528x + -0.00787x2 Reorder the terms: -72.89 + 1.528x + -0.00787x2 = 72.89 + -72.89 + -1.528x + 1.528x + 0.00787x2 + -0.00787x2 Combine like terms: 72.89 + -72.89 = 0.00 -72.89 + 1.528x + -0.00787x2 = 0.00 + -1.528x + 1.528x + 0.00787x2 + -0.00787x2 -72.89 + 1.528x + -0.00787x2 = -1.528x + 1.528x + 0.00787x2 + -0.00787x2 Combine like terms: -1.528x + 1.528x = 0.000 -72.89 + 1.528x + -0.00787x2 = 0.000 + 0.00787x2 + -0.00787x2 -72.89 + 1.528x + -0.00787x2 = 0.00787x2 + -0.00787x2 Combine like terms: 0.00787x2 + -0.00787x2 = 0.00000 -72.89 + 1.528x + -0.00787x2 = 0.00000 Begin completing the square. Divide all terms by -0.00787 the coefficient of the squared term: Divide each side by '-0.00787'. 9261.753494 + -194.1550191x + x2 = 0 Move the constant term to the right: Add '-9261.753494' to each side of the equation. 9261.753494 + -194.1550191x + -9261.753494 + x2 = 0 + -9261.753494 Reorder the terms: 9261.753494 + -9261.753494 + -194.1550191x + x2 = 0 + -9261.753494 Combine like terms: 9261.753494 + -9261.753494 = 0.000000 0.000000 + -194.1550191x + x2 = 0 + -9261.753494 -194.1550191x + x2 = 0 + -9261.753494 Combine like terms: 0 + -9261.753494 = -9261.753494 -194.1550191x + x2 = -9261.753494 The x term is -194.1550191x. Take half its coefficient (-97.07750955). Square it (9424.042860) and add it to both sides. Add '9424.042860' to each side of the equation. -194.1550191x + 9424.042860 + x2 = -9261.753494 + 9424.042860 Reorder the terms: 9424.042860 + -194.1550191x + x2 = -9261.753494 + 9424.042860 Combine like terms: -9261.753494 + 9424.042860 = 162.289366 9424.042860 + -194.1550191x + x2 = 162.289366 Factor a perfect square on the left side: (x + -97.07750955)(x + -97.07750955) = 162.289366 Calculate the square root of the right side: 12.73928436 Break this problem into two subproblems by setting (x + -97.07750955) equal to 12.73928436 and -12.73928436.Subproblem 1
x + -97.07750955 = 12.73928436 Simplifying x + -97.07750955 = 12.73928436 Reorder the terms: -97.07750955 + x = 12.73928436 Solving -97.07750955 + x = 12.73928436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '97.07750955' to each side of the equation. -97.07750955 + 97.07750955 + x = 12.73928436 + 97.07750955 Combine like terms: -97.07750955 + 97.07750955 = 0.00000000 0.00000000 + x = 12.73928436 + 97.07750955 x = 12.73928436 + 97.07750955 Combine like terms: 12.73928436 + 97.07750955 = 109.81679391 x = 109.81679391 Simplifying x = 109.81679391Subproblem 2
x + -97.07750955 = -12.73928436 Simplifying x + -97.07750955 = -12.73928436 Reorder the terms: -97.07750955 + x = -12.73928436 Solving -97.07750955 + x = -12.73928436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '97.07750955' to each side of the equation. -97.07750955 + 97.07750955 + x = -12.73928436 + 97.07750955 Combine like terms: -97.07750955 + 97.07750955 = 0.00000000 0.00000000 + x = -12.73928436 + 97.07750955 x = -12.73928436 + 97.07750955 Combine like terms: -12.73928436 + 97.07750955 = 84.33822519 x = 84.33822519 Simplifying x = 84.33822519Solution
The solution to the problem is based on the solutions from the subproblems. x = {109.81679391, 84.33822519}
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