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Simplifying -0.08x2 + 1.6x + -1.5 = 0 Reorder the terms: -1.5 + 1.6x + -0.08x2 = 0 Solving -1.5 + 1.6x + -0.08x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.08 the coefficient of the squared term: Divide each side by '-0.08'. 18.75 + -20x + x2 = 0 Move the constant term to the right: Add '-18.75' to each side of the equation. 18.75 + -20x + -18.75 + x2 = 0 + -18.75 Reorder the terms: 18.75 + -18.75 + -20x + x2 = 0 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + -20x + x2 = 0 + -18.75 -20x + x2 = 0 + -18.75 Combine like terms: 0 + -18.75 = -18.75 -20x + x2 = -18.75 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -18.75 + 100 Reorder the terms: 100 + -20x + x2 = -18.75 + 100 Combine like terms: -18.75 + 100 = 81.25 100 + -20x + x2 = 81.25 Factor a perfect square on the left side: (x + -10)(x + -10) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + -10) equal to 9.013878189 and -9.013878189.Subproblem 1
x + -10 = 9.013878189 Simplifying x + -10 = 9.013878189 Reorder the terms: -10 + x = 9.013878189 Solving -10 + x = 9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.013878189 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.013878189 + 10 x = 9.013878189 + 10 Combine like terms: 9.013878189 + 10 = 19.013878189 x = 19.013878189 Simplifying x = 19.013878189Subproblem 2
x + -10 = -9.013878189 Simplifying x + -10 = -9.013878189 Reorder the terms: -10 + x = -9.013878189 Solving -10 + x = -9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.013878189 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.013878189 + 10 x = -9.013878189 + 10 Combine like terms: -9.013878189 + 10 = 0.986121811 x = 0.986121811 Simplifying x = 0.986121811Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.013878189, 0.986121811}
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