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Simplifying 0 = x2 + -260x + -175 Reorder the terms: 0 = -175 + -260x + x2 Solving 0 = -175 + -260x + x2 Solving for variable 'x'. Combine like terms: 0 + 175 = 175 175 + 260x + -1x2 = -175 + -260x + x2 + 175 + 260x + -1x2 Reorder the terms: 175 + 260x + -1x2 = -175 + 175 + -260x + 260x + x2 + -1x2 Combine like terms: -175 + 175 = 0 175 + 260x + -1x2 = 0 + -260x + 260x + x2 + -1x2 175 + 260x + -1x2 = -260x + 260x + x2 + -1x2 Combine like terms: -260x + 260x = 0 175 + 260x + -1x2 = 0 + x2 + -1x2 175 + 260x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 175 + 260x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -175 + -260x + x2 = 0 Move the constant term to the right: Add '175' to each side of the equation. -175 + -260x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + -260x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + -260x + x2 = 0 + 175 -260x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 -260x + x2 = 175 The x term is -260x. Take half its coefficient (-130). Square it (16900) and add it to both sides. Add '16900' to each side of the equation. -260x + 16900 + x2 = 175 + 16900 Reorder the terms: 16900 + -260x + x2 = 175 + 16900 Combine like terms: 175 + 16900 = 17075 16900 + -260x + x2 = 17075 Factor a perfect square on the left side: (x + -130)(x + -130) = 17075 Calculate the square root of the right side: 130.671343454 Break this problem into two subproblems by setting (x + -130) equal to 130.671343454 and -130.671343454.Subproblem 1
x + -130 = 130.671343454 Simplifying x + -130 = 130.671343454 Reorder the terms: -130 + x = 130.671343454 Solving -130 + x = 130.671343454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '130' to each side of the equation. -130 + 130 + x = 130.671343454 + 130 Combine like terms: -130 + 130 = 0 0 + x = 130.671343454 + 130 x = 130.671343454 + 130 Combine like terms: 130.671343454 + 130 = 260.671343454 x = 260.671343454 Simplifying x = 260.671343454Subproblem 2
x + -130 = -130.671343454 Simplifying x + -130 = -130.671343454 Reorder the terms: -130 + x = -130.671343454 Solving -130 + x = -130.671343454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '130' to each side of the equation. -130 + 130 + x = -130.671343454 + 130 Combine like terms: -130 + 130 = 0 0 + x = -130.671343454 + 130 x = -130.671343454 + 130 Combine like terms: -130.671343454 + 130 = -0.671343454 x = -0.671343454 Simplifying x = -0.671343454Solution
The solution to the problem is based on the solutions from the subproblems. x = {260.671343454, -0.671343454}
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