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Simplifying 154 = (x + 10)(x + -7) Reorder the terms: 154 = (10 + x)(x + -7) Reorder the terms: 154 = (10 + x)(-7 + x) Multiply (10 + x) * (-7 + x) 154 = (10(-7 + x) + x(-7 + x)) 154 = ((-7 * 10 + x * 10) + x(-7 + x)) 154 = ((-70 + 10x) + x(-7 + x)) 154 = (-70 + 10x + (-7 * x + x * x)) 154 = (-70 + 10x + (-7x + x2)) Combine like terms: 10x + -7x = 3x 154 = (-70 + 3x + x2) Solving 154 = -70 + 3x + x2 Solving for variable 'x'. Combine like terms: 154 + 70 = 224 224 + -3x + -1x2 = -70 + 3x + x2 + 70 + -3x + -1x2 Reorder the terms: 224 + -3x + -1x2 = -70 + 70 + 3x + -3x + x2 + -1x2 Combine like terms: -70 + 70 = 0 224 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2 224 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 224 + -3x + -1x2 = 0 + x2 + -1x2 224 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 224 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -224 + 3x + x2 = 0 Move the constant term to the right: Add '224' to each side of the equation. -224 + 3x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + 3x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + 3x + x2 = 0 + 224 3x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 3x + x2 = 224 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 = 224 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 224 + 2.25 Combine like terms: 224 + 2.25 = 226.25 2.25 + 3x + x2 = 226.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 226.25 Calculate the square root of the right side: 15.041608956 Break this problem into two subproblems by setting (x + 1.5) equal to 15.041608956 and -15.041608956.Subproblem 1
x + 1.5 = 15.041608956 Simplifying x + 1.5 = 15.041608956 Reorder the terms: 1.5 + x = 15.041608956 Solving 1.5 + x = 15.041608956 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 = 15.041608956 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 15.041608956 + -1.5 x = 15.041608956 + -1.5 Combine like terms: 15.041608956 + -1.5 = 13.541608956 x = 13.541608956 Simplifying x = 13.541608956Subproblem 2
x + 1.5 = -15.041608956 Simplifying x + 1.5 = -15.041608956 Reorder the terms: 1.5 + x = -15.041608956 Solving 1.5 + x = -15.041608956 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 = -15.041608956 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -15.041608956 + -1.5 x = -15.041608956 + -1.5 Combine like terms: -15.041608956 + -1.5 = -16.541608956 x = -16.541608956 Simplifying x = -16.541608956Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.541608956, -16.541608956}
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