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Simplifying 2x2 + -14x = 90 Reorder the terms: -14x + 2x2 = 90 Solving -14x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -14x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -7x + x2)' equal to zero and attempt to solve: Simplifying -45 + -7x + x2 = 0 Solving -45 + -7x + x2 = 0 Begin completing the square. 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 = 11.066372975 x = 11.066372975 Simplifying x = 11.066372975Subproblem 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 = -4.066372975 x = -4.066372975 Simplifying x = -4.066372975Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.066372975, -4.066372975}Solution
x = {11.066372975, -4.066372975}
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