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Simplifying 4x2 + -16x + -525 = 0 Reorder the terms: -525 + -16x + 4x2 = 0 Solving -525 + -16x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -131.25 + -4x + x2 = 0 Move the constant term to the right: Add '131.25' to each side of the equation. -131.25 + -4x + 131.25 + x2 = 0 + 131.25 Reorder the terms: -131.25 + 131.25 + -4x + x2 = 0 + 131.25 Combine like terms: -131.25 + 131.25 = 0.00 0.00 + -4x + x2 = 0 + 131.25 -4x + x2 = 0 + 131.25 Combine like terms: 0 + 131.25 = 131.25 -4x + x2 = 131.25 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 131.25 + 4 Reorder the terms: 4 + -4x + x2 = 131.25 + 4 Combine like terms: 131.25 + 4 = 135.25 4 + -4x + x2 = 135.25 Factor a perfect square on the left side: (x + -2)(x + -2) = 135.25 Calculate the square root of the right side: 11.62970335 Break this problem into two subproblems by setting (x + -2) equal to 11.62970335 and -11.62970335.Subproblem 1
x + -2 = 11.62970335 Simplifying x + -2 = 11.62970335 Reorder the terms: -2 + x = 11.62970335 Solving -2 + x = 11.62970335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 11.62970335 + 2 Combine like terms: -2 + 2 = 0 0 + x = 11.62970335 + 2 x = 11.62970335 + 2 Combine like terms: 11.62970335 + 2 = 13.62970335 x = 13.62970335 Simplifying x = 13.62970335Subproblem 2
x + -2 = -11.62970335 Simplifying x + -2 = -11.62970335 Reorder the terms: -2 + x = -11.62970335 Solving -2 + x = -11.62970335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -11.62970335 + 2 Combine like terms: -2 + 2 = 0 0 + x = -11.62970335 + 2 x = -11.62970335 + 2 Combine like terms: -11.62970335 + 2 = -9.62970335 x = -9.62970335 Simplifying x = -9.62970335Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.62970335, -9.62970335}
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