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Simplifying -8x2 + 3x + 8 + 6x + 10 = 0 Reorder the terms: 8 + 10 + 3x + 6x + -8x2 = 0 Combine like terms: 8 + 10 = 18 18 + 3x + 6x + -8x2 = 0 Combine like terms: 3x + 6x = 9x 18 + 9x + -8x2 = 0 Solving 18 + 9x + -8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -2.25 + -1.125x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -1.125x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -1.125x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -1.125x + x2 = 0 + 2.25 -1.125x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -1.125x + x2 = 2.25 The x term is -1.125x. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x + 0.31640625 + x2 = 2.25 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 2.25 + 0.31640625 Combine like terms: 2.25 + 0.31640625 = 2.56640625 0.31640625 + -1.125x + x2 = 2.56640625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 2.56640625 Calculate the square root of the right side: 1.602000702 Break this problem into two subproblems by setting (x + -0.5625) equal to 1.602000702 and -1.602000702.Subproblem 1
x + -0.5625 = 1.602000702 Simplifying x + -0.5625 = 1.602000702 Reorder the terms: -0.5625 + x = 1.602000702 Solving -0.5625 + x = 1.602000702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 1.602000702 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 1.602000702 + 0.5625 x = 1.602000702 + 0.5625 Combine like terms: 1.602000702 + 0.5625 = 2.164500702 x = 2.164500702 Simplifying x = 2.164500702Subproblem 2
x + -0.5625 = -1.602000702 Simplifying x + -0.5625 = -1.602000702 Reorder the terms: -0.5625 + x = -1.602000702 Solving -0.5625 + x = -1.602000702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -1.602000702 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -1.602000702 + 0.5625 x = -1.602000702 + 0.5625 Combine like terms: -1.602000702 + 0.5625 = -1.039500702 x = -1.039500702 Simplifying x = -1.039500702Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.164500702, -1.039500702}
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