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Simplifying 5x2 + -5x + 10 = x2 + 10x Reorder the terms: 10 + -5x + 5x2 = x2 + 10x Reorder the terms: 10 + -5x + 5x2 = 10x + x2 Solving 10 + -5x + 5x2 = 10x + x2 Solving for variable 'x'. Reorder the terms: 10 + -5x + -10x + 5x2 + -1x2 = 10x + x2 + -10x + -1x2 Combine like terms: -5x + -10x = -15x 10 + -15x + 5x2 + -1x2 = 10x + x2 + -10x + -1x2 Combine like terms: 5x2 + -1x2 = 4x2 10 + -15x + 4x2 = 10x + x2 + -10x + -1x2 Reorder the terms: 10 + -15x + 4x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 10 + -15x + 4x2 = 0 + x2 + -1x2 10 + -15x + 4x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10 + -15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.5 + -3.75x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -3.75x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -3.75x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -3.75x + x2 = 0 + -2.5 -3.75x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -3.75x + x2 = -2.5 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = -2.5 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = -2.5 + 3.515625 Combine like terms: -2.5 + 3.515625 = 1.015625 3.515625 + -3.75x + x2 = 1.015625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (x + -1.875) equal to 1.007782219 and -1.007782219.Subproblem 1
x + -1.875 = 1.007782219 Simplifying x + -1.875 = 1.007782219 Reorder the terms: -1.875 + x = 1.007782219 Solving -1.875 + x = 1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 1.007782219 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 1.007782219 + 1.875 x = 1.007782219 + 1.875 Combine like terms: 1.007782219 + 1.875 = 2.882782219 x = 2.882782219 Simplifying x = 2.882782219Subproblem 2
x + -1.875 = -1.007782219 Simplifying x + -1.875 = -1.007782219 Reorder the terms: -1.875 + x = -1.007782219 Solving -1.875 + x = -1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -1.007782219 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -1.007782219 + 1.875 x = -1.007782219 + 1.875 Combine like terms: -1.007782219 + 1.875 = 0.867217781 x = 0.867217781 Simplifying x = 0.867217781Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.882782219, 0.867217781}
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