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Simplifying -16x2 + 35x + -12 = 0 Reorder the terms: -12 + 35x + -16x2 = 0 Solving -12 + 35x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.75 + -2.1875x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -2.1875x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -2.1875x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -2.1875x + x2 = 0 + -0.75 -2.1875x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -2.1875x + x2 = -0.75 The x term is -2.1875x. Take half its coefficient (-1.09375). Square it (1.196289063) and add it to both sides. Add '1.196289063' to each side of the equation. -2.1875x + 1.196289063 + x2 = -0.75 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875x + x2 = -0.75 + 1.196289063 Combine like terms: -0.75 + 1.196289063 = 0.446289063 1.196289063 + -2.1875x + x2 = 0.446289063 Factor a perfect square on the left side: (x + -1.09375)(x + -1.09375) = 0.446289063 Calculate the square root of the right side: 0.668048698 Break this problem into two subproblems by setting (x + -1.09375) equal to 0.668048698 and -0.668048698.Subproblem 1
x + -1.09375 = 0.668048698 Simplifying x + -1.09375 = 0.668048698 Reorder the terms: -1.09375 + x = 0.668048698 Solving -1.09375 + x = 0.668048698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + x = 0.668048698 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = 0.668048698 + 1.09375 x = 0.668048698 + 1.09375 Combine like terms: 0.668048698 + 1.09375 = 1.761798698 x = 1.761798698 Simplifying x = 1.761798698Subproblem 2
x + -1.09375 = -0.668048698 Simplifying x + -1.09375 = -0.668048698 Reorder the terms: -1.09375 + x = -0.668048698 Solving -1.09375 + x = -0.668048698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + x = -0.668048698 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = -0.668048698 + 1.09375 x = -0.668048698 + 1.09375 Combine like terms: -0.668048698 + 1.09375 = 0.425701302 x = 0.425701302 Simplifying x = 0.425701302Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.761798698, 0.425701302}
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