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Simplifying 4x2 + -10x = x2 + -1x + -4 Reorder the terms: -10x + 4x2 = x2 + -1x + -4 Reorder the terms: -10x + 4x2 = -4 + -1x + x2 Solving -10x + 4x2 = -4 + -1x + x2 Solving for variable 'x'. Reorder the terms: 4 + -10x + x + 4x2 + -1x2 = -4 + -1x + x2 + 4 + x + -1x2 Combine like terms: -10x + x = -9x 4 + -9x + 4x2 + -1x2 = -4 + -1x + x2 + 4 + x + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 4 + -9x + 3x2 = -4 + -1x + x2 + 4 + x + -1x2 Reorder the terms: 4 + -9x + 3x2 = -4 + 4 + -1x + x + x2 + -1x2 Combine like terms: -4 + 4 = 0 4 + -9x + 3x2 = 0 + -1x + x + x2 + -1x2 4 + -9x + 3x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 4 + -9x + 3x2 = 0 + x2 + -1x2 4 + -9x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4 + -9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + -3x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -3x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -3x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -3x + x2 = 0 + -1.333333333 -3x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -3x + x2 = -1.333333333 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.333333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.333333333 + 2.25 Combine like terms: -1.333333333 + 2.25 = 0.916666667 2.25 + -3x + x2 = 0.916666667 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.916666667 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (x + -1.5) equal to 0.957427108 and -0.957427108.Subproblem 1
x + -1.5 = 0.957427108 Simplifying x + -1.5 = 0.957427108 Reorder the terms: -1.5 + x = 0.957427108 Solving -1.5 + x = 0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.957427108 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.957427108 + 1.5 x = 0.957427108 + 1.5 Combine like terms: 0.957427108 + 1.5 = 2.457427108 x = 2.457427108 Simplifying x = 2.457427108Subproblem 2
x + -1.5 = -0.957427108 Simplifying x + -1.5 = -0.957427108 Reorder the terms: -1.5 + x = -0.957427108 Solving -1.5 + x = -0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.957427108 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.957427108 + 1.5 x = -0.957427108 + 1.5 Combine like terms: -0.957427108 + 1.5 = 0.542572892 x = 0.542572892 Simplifying x = 0.542572892Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.457427108, 0.542572892}
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