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Simplifying 20 = -0.1x2 + 3.2x + -3.5 Reorder the terms: 20 = -3.5 + 3.2x + -0.1x2 Solving 20 = -3.5 + 3.2x + -0.1x2 Solving for variable 'x'. Combine like terms: 20 + 3.5 = 23.5 23.5 + -3.2x + 0.1x2 = -3.5 + 3.2x + -0.1x2 + 3.5 + -3.2x + 0.1x2 Reorder the terms: 23.5 + -3.2x + 0.1x2 = -3.5 + 3.5 + 3.2x + -3.2x + -0.1x2 + 0.1x2 Combine like terms: -3.5 + 3.5 = 0.0 23.5 + -3.2x + 0.1x2 = 0.0 + 3.2x + -3.2x + -0.1x2 + 0.1x2 23.5 + -3.2x + 0.1x2 = 3.2x + -3.2x + -0.1x2 + 0.1x2 Combine like terms: 3.2x + -3.2x = 0.0 23.5 + -3.2x + 0.1x2 = 0.0 + -0.1x2 + 0.1x2 23.5 + -3.2x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 23.5 + -3.2x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 235 + -32x + x2 = 0 Move the constant term to the right: Add '-235' to each side of the equation. 235 + -32x + -235 + x2 = 0 + -235 Reorder the terms: 235 + -235 + -32x + x2 = 0 + -235 Combine like terms: 235 + -235 = 0 0 + -32x + x2 = 0 + -235 -32x + x2 = 0 + -235 Combine like terms: 0 + -235 = -235 -32x + x2 = -235 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -235 + 256 Reorder the terms: 256 + -32x + x2 = -235 + 256 Combine like terms: -235 + 256 = 21 256 + -32x + x2 = 21 Factor a perfect square on the left side: (x + -16)(x + -16) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + -16) equal to 4.582575695 and -4.582575695.Subproblem 1
x + -16 = 4.582575695 Simplifying x + -16 = 4.582575695 Reorder the terms: -16 + x = 4.582575695 Solving -16 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 4.582575695 + 16 Combine like terms: -16 + 16 = 0 0 + x = 4.582575695 + 16 x = 4.582575695 + 16 Combine like terms: 4.582575695 + 16 = 20.582575695 x = 20.582575695 Simplifying x = 20.582575695Subproblem 2
x + -16 = -4.582575695 Simplifying x + -16 = -4.582575695 Reorder the terms: -16 + x = -4.582575695 Solving -16 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -4.582575695 + 16 Combine like terms: -16 + 16 = 0 0 + x = -4.582575695 + 16 x = -4.582575695 + 16 Combine like terms: -4.582575695 + 16 = 11.417424305 x = 11.417424305 Simplifying x = 11.417424305Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.582575695, 11.417424305}
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