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Simplifying 3.5 = -16x2 + 56x Reorder the terms: 3.5 = 56x + -16x2 Solving 3.5 = 56x + -16x2 Solving for variable 'x'. Reorder the terms: 3.5 + -56x + 16x2 = 56x + -56x + -16x2 + 16x2 Combine like terms: 56x + -56x = 0 3.5 + -56x + 16x2 = 0 + -16x2 + 16x2 3.5 + -56x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 3.5 + -56x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.21875 + -3.5x + x2 = 0 Move the constant term to the right: Add '-0.21875' to each side of the equation. 0.21875 + -3.5x + -0.21875 + x2 = 0 + -0.21875 Reorder the terms: 0.21875 + -0.21875 + -3.5x + x2 = 0 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + -3.5x + x2 = 0 + -0.21875 -3.5x + x2 = 0 + -0.21875 Combine like terms: 0 + -0.21875 = -0.21875 -3.5x + x2 = -0.21875 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -0.21875 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -0.21875 + 3.0625 Combine like terms: -0.21875 + 3.0625 = 2.84375 3.0625 + -3.5x + x2 = 2.84375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 2.84375 Calculate the square root of the right side: 1.686342195 Break this problem into two subproblems by setting (x + -1.75) equal to 1.686342195 and -1.686342195.Subproblem 1
x + -1.75 = 1.686342195 Simplifying x + -1.75 = 1.686342195 Reorder the terms: -1.75 + x = 1.686342195 Solving -1.75 + x = 1.686342195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.686342195 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.686342195 + 1.75 x = 1.686342195 + 1.75 Combine like terms: 1.686342195 + 1.75 = 3.436342195 x = 3.436342195 Simplifying x = 3.436342195Subproblem 2
x + -1.75 = -1.686342195 Simplifying x + -1.75 = -1.686342195 Reorder the terms: -1.75 + x = -1.686342195 Solving -1.75 + x = -1.686342195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.686342195 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.686342195 + 1.75 x = -1.686342195 + 1.75 Combine like terms: -1.686342195 + 1.75 = 0.063657805 x = 0.063657805 Simplifying x = 0.063657805Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.436342195, 0.063657805}
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