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Simplifying 0.23(4x2 + 9x + -4) + 0.9(0.04x2 + 3x + -7) = 0 Reorder the terms: 0.23(-4 + 9x + 4x2) + 0.9(0.04x2 + 3x + -7) = 0 (-4 * 0.23 + 9x * 0.23 + 4x2 * 0.23) + 0.9(0.04x2 + 3x + -7) = 0 (-0.92 + 2.07x + 0.92x2) + 0.9(0.04x2 + 3x + -7) = 0 Reorder the terms: -0.92 + 2.07x + 0.92x2 + 0.9(-7 + 3x + 0.04x2) = 0 -0.92 + 2.07x + 0.92x2 + (-7 * 0.9 + 3x * 0.9 + 0.04x2 * 0.9) = 0 -0.92 + 2.07x + 0.92x2 + (-6.3 + 2.7x + 0.036x2) = 0 Reorder the terms: -0.92 + -6.3 + 2.07x + 2.7x + 0.92x2 + 0.036x2 = 0 Combine like terms: -0.92 + -6.3 = -7.22 -7.22 + 2.07x + 2.7x + 0.92x2 + 0.036x2 = 0 Combine like terms: 2.07x + 2.7x = 4.77x -7.22 + 4.77x + 0.92x2 + 0.036x2 = 0 Combine like terms: 0.92x2 + 0.036x2 = 0.956x2 -7.22 + 4.77x + 0.956x2 = 0 Solving -7.22 + 4.77x + 0.956x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.956 the coefficient of the squared term: Divide each side by '0.956'. -7.552301255 + 4.989539749x + x2 = 0 Move the constant term to the right: Add '7.552301255' to each side of the equation. -7.552301255 + 4.989539749x + 7.552301255 + x2 = 0 + 7.552301255 Reorder the terms: -7.552301255 + 7.552301255 + 4.989539749x + x2 = 0 + 7.552301255 Combine like terms: -7.552301255 + 7.552301255 = 0.000000000 0.000000000 + 4.989539749x + x2 = 0 + 7.552301255 4.989539749x + x2 = 0 + 7.552301255 Combine like terms: 0 + 7.552301255 = 7.552301255 4.989539749x + x2 = 7.552301255 The x term is 4.989539749x. Take half its coefficient (2.494769875). Square it (6.223876729) and add it to both sides. Add '6.223876729' to each side of the equation. 4.989539749x + 6.223876729 + x2 = 7.552301255 + 6.223876729 Reorder the terms: 6.223876729 + 4.989539749x + x2 = 7.552301255 + 6.223876729 Combine like terms: 7.552301255 + 6.223876729 = 13.776177984 6.223876729 + 4.989539749x + x2 = 13.776177984 Factor a perfect square on the left side: (x + 2.494769875)(x + 2.494769875) = 13.776177984 Calculate the square root of the right side: 3.711627404 Break this problem into two subproblems by setting (x + 2.494769875) equal to 3.711627404 and -3.711627404.Subproblem 1
x + 2.494769875 = 3.711627404 Simplifying x + 2.494769875 = 3.711627404 Reorder the terms: 2.494769875 + x = 3.711627404 Solving 2.494769875 + x = 3.711627404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.494769875' to each side of the equation. 2.494769875 + -2.494769875 + x = 3.711627404 + -2.494769875 Combine like terms: 2.494769875 + -2.494769875 = 0.000000000 0.000000000 + x = 3.711627404 + -2.494769875 x = 3.711627404 + -2.494769875 Combine like terms: 3.711627404 + -2.494769875 = 1.216857529 x = 1.216857529 Simplifying x = 1.216857529Subproblem 2
x + 2.494769875 = -3.711627404 Simplifying x + 2.494769875 = -3.711627404 Reorder the terms: 2.494769875 + x = -3.711627404 Solving 2.494769875 + x = -3.711627404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.494769875' to each side of the equation. 2.494769875 + -2.494769875 + x = -3.711627404 + -2.494769875 Combine like terms: 2.494769875 + -2.494769875 = 0.000000000 0.000000000 + x = -3.711627404 + -2.494769875 x = -3.711627404 + -2.494769875 Combine like terms: -3.711627404 + -2.494769875 = -6.206397279 x = -6.206397279 Simplifying x = -6.206397279Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.216857529, -6.206397279}
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