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Simplifying (4x2 + 3x + -9) + (-9x + -10) = 0 Reorder the terms: (-9 + 3x + 4x2) + (-9x + -10) = 0 Remove parenthesis around (-9 + 3x + 4x2) -9 + 3x + 4x2 + (-9x + -10) = 0 Reorder the terms: -9 + 3x + 4x2 + (-10 + -9x) = 0 Remove parenthesis around (-10 + -9x) -9 + 3x + 4x2 + -10 + -9x = 0 Reorder the terms: -9 + -10 + 3x + -9x + 4x2 = 0 Combine like terms: -9 + -10 = -19 -19 + 3x + -9x + 4x2 = 0 Combine like terms: 3x + -9x = -6x -19 + -6x + 4x2 = 0 Solving -19 + -6x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.75 + -1.5x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -1.5x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + -1.5x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -1.5x + x2 = 0 + 4.75 -1.5x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 -1.5x + x2 = 4.75 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 4.75 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 4.75 + 0.5625 Combine like terms: 4.75 + 0.5625 = 5.3125 0.5625 + -1.5x + x2 = 5.3125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 5.3125 Calculate the square root of the right side: 2.304886114 Break this problem into two subproblems by setting (x + -0.75) equal to 2.304886114 and -2.304886114.Subproblem 1
x + -0.75 = 2.304886114 Simplifying x + -0.75 = 2.304886114 Reorder the terms: -0.75 + x = 2.304886114 Solving -0.75 + x = 2.304886114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.304886114 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.304886114 + 0.75 x = 2.304886114 + 0.75 Combine like terms: 2.304886114 + 0.75 = 3.054886114 x = 3.054886114 Simplifying x = 3.054886114Subproblem 2
x + -0.75 = -2.304886114 Simplifying x + -0.75 = -2.304886114 Reorder the terms: -0.75 + x = -2.304886114 Solving -0.75 + x = -2.304886114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.304886114 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.304886114 + 0.75 x = -2.304886114 + 0.75 Combine like terms: -2.304886114 + 0.75 = -1.554886114 x = -1.554886114 Simplifying x = -1.554886114Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.054886114, -1.554886114}
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