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Simplifying 10x2 + -32x = 9 Reorder the terms: -32x + 10x2 = 9 Solving -32x + 10x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -32x + 10x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -32x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + -3.2x + x2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + -3.2x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + -3.2x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + -3.2x + x2 = 0 + 0.9 -3.2x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 -3.2x + x2 = 0.9 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 0.9 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 0.9 + 2.56 Combine like terms: 0.9 + 2.56 = 3.46 2.56 + -3.2x + x2 = 3.46 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 3.46 Calculate the square root of the right side: 1.860107524 Break this problem into two subproblems by setting (x + -1.6) equal to 1.860107524 and -1.860107524.Subproblem 1
x + -1.6 = 1.860107524 Simplifying x + -1.6 = 1.860107524 Reorder the terms: -1.6 + x = 1.860107524 Solving -1.6 + x = 1.860107524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 1.860107524 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 1.860107524 + 1.6 x = 1.860107524 + 1.6 Combine like terms: 1.860107524 + 1.6 = 3.460107524 x = 3.460107524 Simplifying x = 3.460107524Subproblem 2
x + -1.6 = -1.860107524 Simplifying x + -1.6 = -1.860107524 Reorder the terms: -1.6 + x = -1.860107524 Solving -1.6 + x = -1.860107524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -1.860107524 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -1.860107524 + 1.6 x = -1.860107524 + 1.6 Combine like terms: -1.860107524 + 1.6 = -0.260107524 x = -0.260107524 Simplifying x = -0.260107524Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.460107524, -0.260107524}
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