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Simplifying -2x2 = 19x + 33 Reorder the terms: -2x2 = 33 + 19x Solving -2x2 = 33 + 19x Solving for variable 'x'. Reorder the terms: -33 + -19x + -2x2 = 33 + 19x + -33 + -19x Reorder the terms: -33 + -19x + -2x2 = 33 + -33 + 19x + -19x Combine like terms: 33 + -33 = 0 -33 + -19x + -2x2 = 0 + 19x + -19x -33 + -19x + -2x2 = 19x + -19x Combine like terms: 19x + -19x = 0 -33 + -19x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(33 + 19x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(33 + 19x + 2x2)' equal to zero and attempt to solve: Simplifying 33 + 19x + 2x2 = 0 Solving 33 + 19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 16.5 + 9.5x + x2 = 0 Move the constant term to the right: Add '-16.5' to each side of the equation. 16.5 + 9.5x + -16.5 + x2 = 0 + -16.5 Reorder the terms: 16.5 + -16.5 + 9.5x + x2 = 0 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + 9.5x + x2 = 0 + -16.5 9.5x + x2 = 0 + -16.5 Combine like terms: 0 + -16.5 = -16.5 9.5x + x2 = -16.5 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = -16.5 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = -16.5 + 22.5625 Combine like terms: -16.5 + 22.5625 = 6.0625 22.5625 + 9.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + 4.75) equal to 2.46221445 and -2.46221445.Subproblem 1
x + 4.75 = 2.46221445 Simplifying x + 4.75 = 2.46221445 Reorder the terms: 4.75 + x = 2.46221445 Solving 4.75 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 2.46221445 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 2.46221445 + -4.75 x = 2.46221445 + -4.75 Combine like terms: 2.46221445 + -4.75 = -2.28778555 x = -2.28778555 Simplifying x = -2.28778555Subproblem 2
x + 4.75 = -2.46221445 Simplifying x + 4.75 = -2.46221445 Reorder the terms: 4.75 + x = -2.46221445 Solving 4.75 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -2.46221445 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -2.46221445 + -4.75 x = -2.46221445 + -4.75 Combine like terms: -2.46221445 + -4.75 = -7.21221445 x = -7.21221445 Simplifying x = -7.21221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.28778555, -7.21221445}Solution
x = {-2.28778555, -7.21221445}
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