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Simplifying (2x) * 2 = x(x + -14) + -5 Remove parenthesis around (2x) 2x * 2 = x(x + -14) + -5 Reorder the terms for easier multiplication: 2 * 2x = x(x + -14) + -5 Multiply 2 * 2 4x = x(x + -14) + -5 Reorder the terms: 4x = x(-14 + x) + -5 4x = (-14 * x + x * x) + -5 4x = (-14x + x2) + -5 Reorder the terms: 4x = -5 + -14x + x2 Solving 4x = -5 + -14x + x2 Solving for variable 'x'. Reorder the terms: 5 + 4x + 14x + -1x2 = -5 + -14x + x2 + 5 + 14x + -1x2 Combine like terms: 4x + 14x = 18x 5 + 18x + -1x2 = -5 + -14x + x2 + 5 + 14x + -1x2 Reorder the terms: 5 + 18x + -1x2 = -5 + 5 + -14x + 14x + x2 + -1x2 Combine like terms: -5 + 5 = 0 5 + 18x + -1x2 = 0 + -14x + 14x + x2 + -1x2 5 + 18x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 5 + 18x + -1x2 = 0 + x2 + -1x2 5 + 18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -18x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -18x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -18x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -18x + x2 = 0 + 5 -18x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -18x + x2 = 5 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 5 + 81 Reorder the terms: 81 + -18x + x2 = 5 + 81 Combine like terms: 5 + 81 = 86 81 + -18x + x2 = 86 Factor a perfect square on the left side: (x + -9)(x + -9) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + -9) equal to 9.273618495 and -9.273618495.Subproblem 1
x + -9 = 9.273618495 Simplifying x + -9 = 9.273618495 Reorder the terms: -9 + x = 9.273618495 Solving -9 + x = 9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 9.273618495 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.273618495 + 9 x = 9.273618495 + 9 Combine like terms: 9.273618495 + 9 = 18.273618495 x = 18.273618495 Simplifying x = 18.273618495Subproblem 2
x + -9 = -9.273618495 Simplifying x + -9 = -9.273618495 Reorder the terms: -9 + x = -9.273618495 Solving -9 + x = -9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -9.273618495 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.273618495 + 9 x = -9.273618495 + 9 Combine like terms: -9.273618495 + 9 = -0.273618495 x = -0.273618495 Simplifying x = -0.273618495Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.273618495, -0.273618495}
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