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Simplifying -0.625x2 + 5x = 9.6 Reorder the terms: 5x + -0.625x2 = 9.6 Solving 5x + -0.625x2 = 9.6 Solving for variable 'x'. Reorder the terms: -9.6 + 5x + -0.625x2 = 9.6 + -9.6 Combine like terms: 9.6 + -9.6 = 0.0 -9.6 + 5x + -0.625x2 = 0.0 Begin completing the square. Divide all terms by -0.625 the coefficient of the squared term: Divide each side by '-0.625'. 15.36 + -8x + x2 = 0 Move the constant term to the right: Add '-15.36' to each side of the equation. 15.36 + -8x + -15.36 + x2 = 0 + -15.36 Reorder the terms: 15.36 + -15.36 + -8x + x2 = 0 + -15.36 Combine like terms: 15.36 + -15.36 = 0.00 0.00 + -8x + x2 = 0 + -15.36 -8x + x2 = 0 + -15.36 Combine like terms: 0 + -15.36 = -15.36 -8x + x2 = -15.36 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -15.36 + 16 Reorder the terms: 16 + -8x + x2 = -15.36 + 16 Combine like terms: -15.36 + 16 = 0.64 16 + -8x + x2 = 0.64 Factor a perfect square on the left side: (x + -4)(x + -4) = 0.64 Calculate the square root of the right side: 0.8 Break this problem into two subproblems by setting (x + -4) equal to 0.8 and -0.8.Subproblem 1
x + -4 = 0.8 Simplifying x + -4 = 0.8 Reorder the terms: -4 + x = 0.8 Solving -4 + x = 0.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0.8 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0.8 + 4 x = 0.8 + 4 Combine like terms: 0.8 + 4 = 4.8 x = 4.8 Simplifying x = 4.8Subproblem 2
x + -4 = -0.8 Simplifying x + -4 = -0.8 Reorder the terms: -4 + x = -0.8 Solving -4 + x = -0.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -0.8 + 4 Combine like terms: -4 + 4 = 0 0 + x = -0.8 + 4 x = -0.8 + 4 Combine like terms: -0.8 + 4 = 3.2 x = 3.2 Simplifying x = 3.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.8, 3.2}
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