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Simplifying 9x2 + -9x + -17 = 1.5 Reorder the terms: -17 + -9x + 9x2 = 1.5 Solving -17 + -9x + 9x2 = 1.5 Solving for variable 'x'. Reorder the terms: -17 + -1.5 + -9x + 9x2 = 1.5 + -1.5 Combine like terms: -17 + -1.5 = -18.5 -18.5 + -9x + 9x2 = 1.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 -18.5 + -9x + 9x2 = 0.0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.055555556 + -1x + x2 = 0.0 Move the constant term to the right: Add '2.055555556' to each side of the equation. -2.055555556 + -1x + 2.055555556 + x2 = 0.0 + 2.055555556 Reorder the terms: -2.055555556 + 2.055555556 + -1x + x2 = 0.0 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + -1x + x2 = 0.0 + 2.055555556 -1x + x2 = 0.0 + 2.055555556 Combine like terms: 0.0 + 2.055555556 = 2.055555556 -1x + x2 = 2.055555556 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.055555556 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.055555556 + 0.25 Combine like terms: 2.055555556 + 0.25 = 2.305555556 0.25 + -1x + x2 = 2.305555556 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.305555556 Calculate the square root of the right side: 1.518405597 Break this problem into two subproblems by setting (x + -0.5) equal to 1.518405597 and -1.518405597.Subproblem 1
x + -0.5 = 1.518405597 Simplifying x + -0.5 = 1.518405597 Reorder the terms: -0.5 + x = 1.518405597 Solving -0.5 + x = 1.518405597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.518405597 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.518405597 + 0.5 x = 1.518405597 + 0.5 Combine like terms: 1.518405597 + 0.5 = 2.018405597 x = 2.018405597 Simplifying x = 2.018405597Subproblem 2
x + -0.5 = -1.518405597 Simplifying x + -0.5 = -1.518405597 Reorder the terms: -0.5 + x = -1.518405597 Solving -0.5 + x = -1.518405597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.518405597 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.518405597 + 0.5 x = -1.518405597 + 0.5 Combine like terms: -1.518405597 + 0.5 = -1.018405597 x = -1.018405597 Simplifying x = -1.018405597Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.018405597, -1.018405597}
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