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Simplifying 3x2 + 5x2 + -9x + -15 = 0 Reorder the terms: -15 + -9x + 3x2 + 5x2 = 0 Combine like terms: 3x2 + 5x2 = 8x2 -15 + -9x + 8x2 = 0 Solving -15 + -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'. -1.875 + -1.125x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -1.125x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -1.125x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -1.125x + x2 = 0 + 1.875 -1.125x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -1.125x + x2 = 1.875 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 = 1.875 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 1.875 + 0.31640625 Combine like terms: 1.875 + 0.31640625 = 2.19140625 0.31640625 + -1.125x + x2 = 2.19140625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 2.19140625 Calculate the square root of the right side: 1.48033991 Break this problem into two subproblems by setting (x + -0.5625) equal to 1.48033991 and -1.48033991.Subproblem 1
x + -0.5625 = 1.48033991 Simplifying x + -0.5625 = 1.48033991 Reorder the terms: -0.5625 + x = 1.48033991 Solving -0.5625 + x = 1.48033991 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 = 1.48033991 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 1.48033991 + 0.5625 x = 1.48033991 + 0.5625 Combine like terms: 1.48033991 + 0.5625 = 2.04283991 x = 2.04283991 Simplifying x = 2.04283991Subproblem 2
x + -0.5625 = -1.48033991 Simplifying x + -0.5625 = -1.48033991 Reorder the terms: -0.5625 + x = -1.48033991 Solving -0.5625 + x = -1.48033991 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 = -1.48033991 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -1.48033991 + 0.5625 x = -1.48033991 + 0.5625 Combine like terms: -1.48033991 + 0.5625 = -0.91783991 x = -0.91783991 Simplifying x = -0.91783991Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.04283991, -0.91783991}
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