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Simplifying (-18x + 120) + -1(4x2 + -5x + 25) = 0 Reorder the terms: (120 + -18x) + -1(4x2 + -5x + 25) = 0 Remove parenthesis around (120 + -18x) 120 + -18x + -1(4x2 + -5x + 25) = 0 Reorder the terms: 120 + -18x + -1(25 + -5x + 4x2) = 0 120 + -18x + (25 * -1 + -5x * -1 + 4x2 * -1) = 0 120 + -18x + (-25 + 5x + -4x2) = 0 Reorder the terms: 120 + -25 + -18x + 5x + -4x2 = 0 Combine like terms: 120 + -25 = 95 95 + -18x + 5x + -4x2 = 0 Combine like terms: -18x + 5x = -13x 95 + -13x + -4x2 = 0 Solving 95 + -13x + -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'. -23.75 + 3.25x + x2 = 0 Move the constant term to the right: Add '23.75' to each side of the equation. -23.75 + 3.25x + 23.75 + x2 = 0 + 23.75 Reorder the terms: -23.75 + 23.75 + 3.25x + x2 = 0 + 23.75 Combine like terms: -23.75 + 23.75 = 0.00 0.00 + 3.25x + x2 = 0 + 23.75 3.25x + x2 = 0 + 23.75 Combine like terms: 0 + 23.75 = 23.75 3.25x + x2 = 23.75 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 23.75 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 23.75 + 2.640625 Combine like terms: 23.75 + 2.640625 = 26.390625 2.640625 + 3.25x + x2 = 26.390625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 26.390625 Calculate the square root of the right side: 5.137180647 Break this problem into two subproblems by setting (x + 1.625) equal to 5.137180647 and -5.137180647.Subproblem 1
x + 1.625 = 5.137180647 Simplifying x + 1.625 = 5.137180647 Reorder the terms: 1.625 + x = 5.137180647 Solving 1.625 + x = 5.137180647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 5.137180647 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 5.137180647 + -1.625 x = 5.137180647 + -1.625 Combine like terms: 5.137180647 + -1.625 = 3.512180647 x = 3.512180647 Simplifying x = 3.512180647Subproblem 2
x + 1.625 = -5.137180647 Simplifying x + 1.625 = -5.137180647 Reorder the terms: 1.625 + x = -5.137180647 Solving 1.625 + x = -5.137180647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -5.137180647 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -5.137180647 + -1.625 x = -5.137180647 + -1.625 Combine like terms: -5.137180647 + -1.625 = -6.762180647 x = -6.762180647 Simplifying x = -6.762180647Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.512180647, -6.762180647}
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