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Simplifying x(130 + -1x) = 130 (130 * x + -1x * x) = 130 (130x + -1x2) = 130 Solving 130x + -1x2 = 130 Solving for variable 'x'. Reorder the terms: -130 + 130x + -1x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + 130x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 130 + -130x + x2 = 0 Move the constant term to the right: Add '-130' to each side of the equation. 130 + -130x + -130 + x2 = 0 + -130 Reorder the terms: 130 + -130 + -130x + x2 = 0 + -130 Combine like terms: 130 + -130 = 0 0 + -130x + x2 = 0 + -130 -130x + x2 = 0 + -130 Combine like terms: 0 + -130 = -130 -130x + x2 = -130 The x term is -130x. Take half its coefficient (-65). Square it (4225) and add it to both sides. Add '4225' to each side of the equation. -130x + 4225 + x2 = -130 + 4225 Reorder the terms: 4225 + -130x + x2 = -130 + 4225 Combine like terms: -130 + 4225 = 4095 4225 + -130x + x2 = 4095 Factor a perfect square on the left side: (x + -65)(x + -65) = 4095 Calculate the square root of the right side: 63.992187023 Break this problem into two subproblems by setting (x + -65) equal to 63.992187023 and -63.992187023.Subproblem 1
x + -65 = 63.992187023 Simplifying x + -65 = 63.992187023 Reorder the terms: -65 + x = 63.992187023 Solving -65 + x = 63.992187023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = 63.992187023 + 65 Combine like terms: -65 + 65 = 0 0 + x = 63.992187023 + 65 x = 63.992187023 + 65 Combine like terms: 63.992187023 + 65 = 128.992187023 x = 128.992187023 Simplifying x = 128.992187023Subproblem 2
x + -65 = -63.992187023 Simplifying x + -65 = -63.992187023 Reorder the terms: -65 + x = -63.992187023 Solving -65 + x = -63.992187023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = -63.992187023 + 65 Combine like terms: -65 + 65 = 0 0 + x = -63.992187023 + 65 x = -63.992187023 + 65 Combine like terms: -63.992187023 + 65 = 1.007812977 x = 1.007812977 Simplifying x = 1.007812977Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.992187023, 1.007812977}
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