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Simplifying 1000 = x2 + 12x + 42 Reorder the terms: 1000 = 42 + 12x + x2 Solving 1000 = 42 + 12x + x2 Solving for variable 'x'. Combine like terms: 1000 + -42 = 958 958 + -12x + -1x2 = 42 + 12x + x2 + -42 + -12x + -1x2 Reorder the terms: 958 + -12x + -1x2 = 42 + -42 + 12x + -12x + x2 + -1x2 Combine like terms: 42 + -42 = 0 958 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2 958 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 958 + -12x + -1x2 = 0 + x2 + -1x2 958 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 958 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -958 + 12x + x2 = 0 Move the constant term to the right: Add '958' to each side of the equation. -958 + 12x + 958 + x2 = 0 + 958 Reorder the terms: -958 + 958 + 12x + x2 = 0 + 958 Combine like terms: -958 + 958 = 0 0 + 12x + x2 = 0 + 958 12x + x2 = 0 + 958 Combine like terms: 0 + 958 = 958 12x + x2 = 958 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 958 + 36 Reorder the terms: 36 + 12x + x2 = 958 + 36 Combine like terms: 958 + 36 = 994 36 + 12x + x2 = 994 Factor a perfect square on the left side: (x + 6)(x + 6) = 994 Calculate the square root of the right side: 31.527765541 Break this problem into two subproblems by setting (x + 6) equal to 31.527765541 and -31.527765541.Subproblem 1
x + 6 = 31.527765541 Simplifying x + 6 = 31.527765541 Reorder the terms: 6 + x = 31.527765541 Solving 6 + x = 31.527765541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 31.527765541 + -6 Combine like terms: 6 + -6 = 0 0 + x = 31.527765541 + -6 x = 31.527765541 + -6 Combine like terms: 31.527765541 + -6 = 25.527765541 x = 25.527765541 Simplifying x = 25.527765541Subproblem 2
x + 6 = -31.527765541 Simplifying x + 6 = -31.527765541 Reorder the terms: 6 + x = -31.527765541 Solving 6 + x = -31.527765541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -31.527765541 + -6 Combine like terms: 6 + -6 = 0 0 + x = -31.527765541 + -6 x = -31.527765541 + -6 Combine like terms: -31.527765541 + -6 = -37.527765541 x = -37.527765541 Simplifying x = -37.527765541Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.527765541, -37.527765541}
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