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Simplifying 0.4x(5 + 2x) + -0.5 = 0.9x + 2.1 (5 * 0.4x + 2x * 0.4x) + -0.5 = 0.9x + 2.1 (2x + 0.8x2) + -0.5 = 0.9x + 2.1 Reorder the terms: -0.5 + 2x + 0.8x2 = 0.9x + 2.1 Reorder the terms: -0.5 + 2x + 0.8x2 = 2.1 + 0.9x Solving -0.5 + 2x + 0.8x2 = 2.1 + 0.9x Solving for variable 'x'. Reorder the terms: -0.5 + -2.1 + 2x + -0.9x + 0.8x2 = 2.1 + 0.9x + -2.1 + -0.9x Combine like terms: -0.5 + -2.1 = -2.6 -2.6 + 2x + -0.9x + 0.8x2 = 2.1 + 0.9x + -2.1 + -0.9x Combine like terms: 2x + -0.9x = 1.1x -2.6 + 1.1x + 0.8x2 = 2.1 + 0.9x + -2.1 + -0.9x Reorder the terms: -2.6 + 1.1x + 0.8x2 = 2.1 + -2.1 + 0.9x + -0.9x Combine like terms: 2.1 + -2.1 = 0.0 -2.6 + 1.1x + 0.8x2 = 0.0 + 0.9x + -0.9x -2.6 + 1.1x + 0.8x2 = 0.9x + -0.9x Combine like terms: 0.9x + -0.9x = 0.0 -2.6 + 1.1x + 0.8x2 = 0.0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -3.25 + 1.375x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 1.375x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 1.375x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 1.375x + x2 = 0 + 3.25 1.375x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 1.375x + x2 = 3.25 The x term is 1.375x. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375x + 0.47265625 + x2 = 3.25 + 0.47265625 Reorder the terms: 0.47265625 + 1.375x + x2 = 3.25 + 0.47265625 Combine like terms: 3.25 + 0.47265625 = 3.72265625 0.47265625 + 1.375x + x2 = 3.72265625 Factor a perfect square on the left side: (x + 0.6875)(x + 0.6875) = 3.72265625 Calculate the square root of the right side: 1.92941863 Break this problem into two subproblems by setting (x + 0.6875) equal to 1.92941863 and -1.92941863.Subproblem 1
x + 0.6875 = 1.92941863 Simplifying x + 0.6875 = 1.92941863 Reorder the terms: 0.6875 + x = 1.92941863 Solving 0.6875 + x = 1.92941863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = 1.92941863 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = 1.92941863 + -0.6875 x = 1.92941863 + -0.6875 Combine like terms: 1.92941863 + -0.6875 = 1.24191863 x = 1.24191863 Simplifying x = 1.24191863Subproblem 2
x + 0.6875 = -1.92941863 Simplifying x + 0.6875 = -1.92941863 Reorder the terms: 0.6875 + x = -1.92941863 Solving 0.6875 + x = -1.92941863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = -1.92941863 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = -1.92941863 + -0.6875 x = -1.92941863 + -0.6875 Combine like terms: -1.92941863 + -0.6875 = -2.61691863 x = -2.61691863 Simplifying x = -2.61691863Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.24191863, -2.61691863}
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