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Simplifying x2 + -9.0x = 15.75 Reorder the terms: -9.0x + x2 = 15.75 Solving -9.0x + x2 = 15.75 Solving for variable 'x'. Reorder the terms: -15.75 + -9.0x + x2 = 15.75 + -15.75 Combine like terms: 15.75 + -15.75 = 0.00 -15.75 + -9.0x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '15.75' to each side of the equation. -15.75 + -9.0x + 15.75 + x2 = 0.00 + 15.75 Reorder the terms: -15.75 + 15.75 + -9.0x + x2 = 0.00 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + -9.0x + x2 = 0.00 + 15.75 -9.0x + x2 = 0.00 + 15.75 Combine like terms: 0.00 + 15.75 = 15.75 -9.0x + x2 = 15.75 The x term is -9.0x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9.0x + 20.25 + x2 = 15.75 + 20.25 Reorder the terms: 20.25 + -9.0x + x2 = 15.75 + 20.25 Combine like terms: 15.75 + 20.25 = 36 20.25 + -9.0x + x2 = 36 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (x + -4.5) equal to 6 and -6.Subproblem 1
x + -4.5 = 6 Simplifying x + -4.5 = 6 Reorder the terms: -4.5 + x = 6 Solving -4.5 + x = 6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 6 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6 + 4.5 x = 6 + 4.5 Combine like terms: 6 + 4.5 = 10.5 x = 10.5 Simplifying x = 10.5Subproblem 2
x + -4.5 = -6 Simplifying x + -4.5 = -6 Reorder the terms: -4.5 + x = -6 Solving -4.5 + x = -6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -6 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6 + 4.5 x = -6 + 4.5 Combine like terms: -6 + 4.5 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.5, -1.5}
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