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Simplifying -11x + 7 = -5x2 + 4x Reorder the terms: 7 + -11x = -5x2 + 4x Reorder the terms: 7 + -11x = 4x + -5x2 Solving 7 + -11x = 4x + -5x2 Solving for variable 'x'. Combine like terms: -11x + -4x = -15x 7 + -15x + 5x2 = 4x + -5x2 + -4x + 5x2 Reorder the terms: 7 + -15x + 5x2 = 4x + -4x + -5x2 + 5x2 Combine like terms: 4x + -4x = 0 7 + -15x + 5x2 = 0 + -5x2 + 5x2 7 + -15x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 7 + -15x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + -3x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -3x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -3x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -3x + x2 = 0 + -1.4 -3x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -3x + x2 = -1.4 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 = -1.4 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.4 + 2.25 Combine like terms: -1.4 + 2.25 = 0.85 2.25 + -3x + x2 = 0.85 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.85 Calculate the square root of the right side: 0.921954446 Break this problem into two subproblems by setting (x + -1.5) equal to 0.921954446 and -0.921954446.Subproblem 1
x + -1.5 = 0.921954446 Simplifying x + -1.5 = 0.921954446 Reorder the terms: -1.5 + x = 0.921954446 Solving -1.5 + x = 0.921954446 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 = 0.921954446 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.921954446 + 1.5 x = 0.921954446 + 1.5 Combine like terms: 0.921954446 + 1.5 = 2.421954446 x = 2.421954446 Simplifying x = 2.421954446Subproblem 2
x + -1.5 = -0.921954446 Simplifying x + -1.5 = -0.921954446 Reorder the terms: -1.5 + x = -0.921954446 Solving -1.5 + x = -0.921954446 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 = -0.921954446 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.921954446 + 1.5 x = -0.921954446 + 1.5 Combine like terms: -0.921954446 + 1.5 = 0.578045554 x = 0.578045554 Simplifying x = 0.578045554Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.421954446, 0.578045554}
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