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Simplifying 1x2 + 15x = 8 Reorder the terms: 15x + 1x2 = 8 Solving 15x + 1x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 15x + 1x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 15x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 15x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 15x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 15x + x2 = 0 + 8 15x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 15x + x2 = 8 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 8 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 8 + 56.25 Combine like terms: 8 + 56.25 = 64.25 56.25 + 15x + x2 = 64.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (x + 7.5) equal to 8.015609771 and -8.015609771.Subproblem 1
x + 7.5 = 8.015609771 Simplifying x + 7.5 = 8.015609771 Reorder the terms: 7.5 + x = 8.015609771 Solving 7.5 + x = 8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 8.015609771 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 8.015609771 + -7.5 x = 8.015609771 + -7.5 Combine like terms: 8.015609771 + -7.5 = 0.515609771 x = 0.515609771 Simplifying x = 0.515609771Subproblem 2
x + 7.5 = -8.015609771 Simplifying x + 7.5 = -8.015609771 Reorder the terms: 7.5 + x = -8.015609771 Solving 7.5 + x = -8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -8.015609771 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -8.015609771 + -7.5 x = -8.015609771 + -7.5 Combine like terms: -8.015609771 + -7.5 = -15.515609771 x = -15.515609771 Simplifying x = -15.515609771Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.515609771, -15.515609771}
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