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Simplifying -2x2 + -14x + 90 = 0 Reorder the terms: 90 + -14x + -2x2 = 0 Solving 90 + -14x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -7x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + -7x + -1x2)' equal to zero and attempt to solve: Simplifying 45 + -7x + -1x2 = 0 Solving 45 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -45 + 7x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 7x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 7x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 7x + x2 = 0 + 45 7x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 7x + x2 = 45 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 45 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 45 + 12.25 Combine like terms: 45 + 12.25 = 57.25 12.25 + 7x + x2 = 57.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (x + 3.5) equal to 7.566372975 and -7.566372975.Subproblem 1
x + 3.5 = 7.566372975 Simplifying x + 3.5 = 7.566372975 Reorder the terms: 3.5 + x = 7.566372975 Solving 3.5 + x = 7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 7.566372975 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 7.566372975 + -3.5 x = 7.566372975 + -3.5 Combine like terms: 7.566372975 + -3.5 = 4.066372975 x = 4.066372975 Simplifying x = 4.066372975Subproblem 2
x + 3.5 = -7.566372975 Simplifying x + 3.5 = -7.566372975 Reorder the terms: 3.5 + x = -7.566372975 Solving 3.5 + x = -7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -7.566372975 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -7.566372975 + -3.5 x = -7.566372975 + -3.5 Combine like terms: -7.566372975 + -3.5 = -11.066372975 x = -11.066372975 Simplifying x = -11.066372975Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.066372975, -11.066372975}Solution
x = {4.066372975, -11.066372975}
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