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Simplifying x(x + -15) + (x + 5) = 15 Reorder the terms: x(-15 + x) + (x + 5) = 15 (-15 * x + x * x) + (x + 5) = 15 (-15x + x2) + (x + 5) = 15 Reorder the terms: -15x + x2 + (5 + x) = 15 Remove parenthesis around (5 + x) -15x + x2 + 5 + x = 15 Reorder the terms: 5 + -15x + x + x2 = 15 Combine like terms: -15x + x = -14x 5 + -14x + x2 = 15 Solving 5 + -14x + x2 = 15 Solving for variable 'x'. Reorder the terms: 5 + -15 + -14x + x2 = 15 + -15 Combine like terms: 5 + -15 = -10 -10 + -14x + x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -10 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -14x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -14x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -14x + x2 = 0 + 10 -14x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -14x + x2 = 10 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 10 + 49 Reorder the terms: 49 + -14x + x2 = 10 + 49 Combine like terms: 10 + 49 = 59 49 + -14x + x2 = 59 Factor a perfect square on the left side: (x + -7)(x + -7) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + -7) equal to 7.681145748 and -7.681145748.Subproblem 1
x + -7 = 7.681145748 Simplifying x + -7 = 7.681145748 Reorder the terms: -7 + x = 7.681145748 Solving -7 + x = 7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 7.681145748 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.681145748 + 7 x = 7.681145748 + 7 Combine like terms: 7.681145748 + 7 = 14.681145748 x = 14.681145748 Simplifying x = 14.681145748Subproblem 2
x + -7 = -7.681145748 Simplifying x + -7 = -7.681145748 Reorder the terms: -7 + x = -7.681145748 Solving -7 + x = -7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -7.681145748 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.681145748 + 7 x = -7.681145748 + 7 Combine like terms: -7.681145748 + 7 = -0.681145748 x = -0.681145748 Simplifying x = -0.681145748Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.681145748, -0.681145748}
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