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Simplifying 0 = -0.08x2 + 1.4x + 32 Reorder the terms: 0 = 32 + 1.4x + -0.08x2 Solving 0 = 32 + 1.4x + -0.08x2 Solving for variable 'x'. Combine like terms: 0 + -32 = -32 -32 + -1.4x + 0.08x2 = 32 + 1.4x + -0.08x2 + -32 + -1.4x + 0.08x2 Reorder the terms: -32 + -1.4x + 0.08x2 = 32 + -32 + 1.4x + -1.4x + -0.08x2 + 0.08x2 Combine like terms: 32 + -32 = 0 -32 + -1.4x + 0.08x2 = 0 + 1.4x + -1.4x + -0.08x2 + 0.08x2 -32 + -1.4x + 0.08x2 = 1.4x + -1.4x + -0.08x2 + 0.08x2 Combine like terms: 1.4x + -1.4x = 0.0 -32 + -1.4x + 0.08x2 = 0.0 + -0.08x2 + 0.08x2 -32 + -1.4x + 0.08x2 = -0.08x2 + 0.08x2 Combine like terms: -0.08x2 + 0.08x2 = 0.00 -32 + -1.4x + 0.08x2 = 0.00 Begin completing the square. Divide all terms by 0.08 the coefficient of the squared term: Divide each side by '0.08'. -400 + -17.5x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + -17.5x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -17.5x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -17.5x + x2 = 0 + 400 -17.5x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -17.5x + x2 = 400 The x term is -17.5x. Take half its coefficient (-8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. -17.5x + 76.5625 + x2 = 400 + 76.5625 Reorder the terms: 76.5625 + -17.5x + x2 = 400 + 76.5625 Combine like terms: 400 + 76.5625 = 476.5625 76.5625 + -17.5x + x2 = 476.5625 Factor a perfect square on the left side: (x + -8.75)(x + -8.75) = 476.5625 Calculate the square root of the right side: 21.830311496 Break this problem into two subproblems by setting (x + -8.75) equal to 21.830311496 and -21.830311496.Subproblem 1
x + -8.75 = 21.830311496 Simplifying x + -8.75 = 21.830311496 Reorder the terms: -8.75 + x = 21.830311496 Solving -8.75 + x = 21.830311496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = 21.830311496 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = 21.830311496 + 8.75 x = 21.830311496 + 8.75 Combine like terms: 21.830311496 + 8.75 = 30.580311496 x = 30.580311496 Simplifying x = 30.580311496Subproblem 2
x + -8.75 = -21.830311496 Simplifying x + -8.75 = -21.830311496 Reorder the terms: -8.75 + x = -21.830311496 Solving -8.75 + x = -21.830311496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = -21.830311496 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = -21.830311496 + 8.75 x = -21.830311496 + 8.75 Combine like terms: -21.830311496 + 8.75 = -13.080311496 x = -13.080311496 Simplifying x = -13.080311496Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.580311496, -13.080311496}
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