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Simplifying (8x2 + -7x + -38) + (9x2 + 9x) = 0 Reorder the terms: (-38 + -7x + 8x2) + (9x2 + 9x) = 0 Remove parenthesis around (-38 + -7x + 8x2) -38 + -7x + 8x2 + (9x2 + 9x) = 0 Reorder the terms: -38 + -7x + 8x2 + (9x + 9x2) = 0 Remove parenthesis around (9x + 9x2) -38 + -7x + 8x2 + 9x + 9x2 = 0 Reorder the terms: -38 + -7x + 9x + 8x2 + 9x2 = 0 Combine like terms: -7x + 9x = 2x -38 + 2x + 8x2 + 9x2 = 0 Combine like terms: 8x2 + 9x2 = 17x2 -38 + 2x + 17x2 = 0 Solving -38 + 2x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -2.235294118 + 0.1176470588x + x2 = 0 Move the constant term to the right: Add '2.235294118' to each side of the equation. -2.235294118 + 0.1176470588x + 2.235294118 + x2 = 0 + 2.235294118 Reorder the terms: -2.235294118 + 2.235294118 + 0.1176470588x + x2 = 0 + 2.235294118 Combine like terms: -2.235294118 + 2.235294118 = 0.000000000 0.000000000 + 0.1176470588x + x2 = 0 + 2.235294118 0.1176470588x + x2 = 0 + 2.235294118 Combine like terms: 0 + 2.235294118 = 2.235294118 0.1176470588x + x2 = 2.235294118 The x term is 0.1176470588x. Take half its coefficient (0.0588235294). Square it (0.003460207611) and add it to both sides. Add '0.003460207611' to each side of the equation. 0.1176470588x + 0.003460207611 + x2 = 2.235294118 + 0.003460207611 Reorder the terms: 0.003460207611 + 0.1176470588x + x2 = 2.235294118 + 0.003460207611 Combine like terms: 2.235294118 + 0.003460207611 = 2.238754325611 0.003460207611 + 0.1176470588x + x2 = 2.238754325611 Factor a perfect square on the left side: (x + 0.0588235294)(x + 0.0588235294) = 2.238754325611 Calculate the square root of the right side: 1.496246746 Break this problem into two subproblems by setting (x + 0.0588235294) equal to 1.496246746 and -1.496246746.Subproblem 1
x + 0.0588235294 = 1.496246746 Simplifying x + 0.0588235294 = 1.496246746 Reorder the terms: 0.0588235294 + x = 1.496246746 Solving 0.0588235294 + x = 1.496246746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + x = 1.496246746 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = 1.496246746 + -0.0588235294 x = 1.496246746 + -0.0588235294 Combine like terms: 1.496246746 + -0.0588235294 = 1.4374232166 x = 1.4374232166 Simplifying x = 1.4374232166Subproblem 2
x + 0.0588235294 = -1.496246746 Simplifying x + 0.0588235294 = -1.496246746 Reorder the terms: 0.0588235294 + x = -1.496246746 Solving 0.0588235294 + x = -1.496246746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + x = -1.496246746 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = -1.496246746 + -0.0588235294 x = -1.496246746 + -0.0588235294 Combine like terms: -1.496246746 + -0.0588235294 = -1.5550702754 x = -1.5550702754 Simplifying x = -1.5550702754Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4374232166, -1.5550702754}
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