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Simplifying 110 = (2x + -3) * x Reorder the terms: 110 = (-3 + 2x) * x Reorder the terms for easier multiplication: 110 = x(-3 + 2x) 110 = (-3 * x + 2x * x) 110 = (-3x + 2x2) Solving 110 = -3x + 2x2 Solving for variable 'x'. Reorder the terms: 110 + 3x + -2x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 110 + 3x + -2x2 = 0 + 2x2 + -2x2 110 + 3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 110 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -55 + -1.5x + x2 = 0 Move the constant term to the right: Add '55' to each side of the equation. -55 + -1.5x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + -1.5x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -1.5x + x2 = 0 + 55 -1.5x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 -1.5x + x2 = 55 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 55 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 55 + 0.5625 Combine like terms: 55 + 0.5625 = 55.5625 0.5625 + -1.5x + x2 = 55.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 55.5625 Calculate the square root of the right side: 7.454025758 Break this problem into two subproblems by setting (x + -0.75) equal to 7.454025758 and -7.454025758.Subproblem 1
x + -0.75 = 7.454025758 Simplifying x + -0.75 = 7.454025758 Reorder the terms: -0.75 + x = 7.454025758 Solving -0.75 + x = 7.454025758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 7.454025758 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 7.454025758 + 0.75 x = 7.454025758 + 0.75 Combine like terms: 7.454025758 + 0.75 = 8.204025758 x = 8.204025758 Simplifying x = 8.204025758Subproblem 2
x + -0.75 = -7.454025758 Simplifying x + -0.75 = -7.454025758 Reorder the terms: -0.75 + x = -7.454025758 Solving -0.75 + x = -7.454025758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -7.454025758 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -7.454025758 + 0.75 x = -7.454025758 + 0.75 Combine like terms: -7.454025758 + 0.75 = -6.704025758 x = -6.704025758 Simplifying x = -6.704025758Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.204025758, -6.704025758}
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