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Simplifying 5x(9 + -1x) = 3[4 + -1(7 + 8x + -9)] (9 * 5x + -1x * 5x) = 3[4 + -1(7 + 8x + -9)] (45x + -5x2) = 3[4 + -1(7 + 8x + -9)] Reorder the terms: 45x + -5x2 = 3[4 + -1(7 + -9 + 8x)] Combine like terms: 7 + -9 = -2 45x + -5x2 = 3[4 + -1(-2 + 8x)] 45x + -5x2 = 3[4 + (-2 * -1 + 8x * -1)] 45x + -5x2 = 3[4 + (2 + -8x)] Combine like terms: 4 + 2 = 6 45x + -5x2 = 3[6 + -8x] 45x + -5x2 = [6 * 3 + -8x * 3] 45x + -5x2 = [18 + -24x] Solving 45x + -5x2 = 18 + -24x Solving for variable 'x'. Reorder the terms: -18 + 45x + 24x + -5x2 = 18 + -24x + -18 + 24x Combine like terms: 45x + 24x = 69x -18 + 69x + -5x2 = 18 + -24x + -18 + 24x Reorder the terms: -18 + 69x + -5x2 = 18 + -18 + -24x + 24x Combine like terms: 18 + -18 = 0 -18 + 69x + -5x2 = 0 + -24x + 24x -18 + 69x + -5x2 = -24x + 24x Combine like terms: -24x + 24x = 0 -18 + 69x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 3.6 + -13.8x + x2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + -13.8x + -3.6 + x2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + -13.8x + x2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + -13.8x + x2 = 0 + -3.6 -13.8x + x2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 -13.8x + x2 = -3.6 The x term is -13.8x. Take half its coefficient (-6.9). Square it (47.61) and add it to both sides. Add '47.61' to each side of the equation. -13.8x + 47.61 + x2 = -3.6 + 47.61 Reorder the terms: 47.61 + -13.8x + x2 = -3.6 + 47.61 Combine like terms: -3.6 + 47.61 = 44.01 47.61 + -13.8x + x2 = 44.01 Factor a perfect square on the left side: (x + -6.9)(x + -6.9) = 44.01 Calculate the square root of the right side: 6.634003316 Break this problem into two subproblems by setting (x + -6.9) equal to 6.634003316 and -6.634003316.Subproblem 1
x + -6.9 = 6.634003316 Simplifying x + -6.9 = 6.634003316 Reorder the terms: -6.9 + x = 6.634003316 Solving -6.9 + x = 6.634003316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.9' to each side of the equation. -6.9 + 6.9 + x = 6.634003316 + 6.9 Combine like terms: -6.9 + 6.9 = 0.0 0.0 + x = 6.634003316 + 6.9 x = 6.634003316 + 6.9 Combine like terms: 6.634003316 + 6.9 = 13.534003316 x = 13.534003316 Simplifying x = 13.534003316Subproblem 2
x + -6.9 = -6.634003316 Simplifying x + -6.9 = -6.634003316 Reorder the terms: -6.9 + x = -6.634003316 Solving -6.9 + x = -6.634003316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.9' to each side of the equation. -6.9 + 6.9 + x = -6.634003316 + 6.9 Combine like terms: -6.9 + 6.9 = 0.0 0.0 + x = -6.634003316 + 6.9 x = -6.634003316 + 6.9 Combine like terms: -6.634003316 + 6.9 = 0.265996684 x = 0.265996684 Simplifying x = 0.265996684Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.534003316, 0.265996684}
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