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Simplifying 5x(10 + -2x) + 8 + -3 = 6x + -3(6 + -1x) + 8x (10 * 5x + -2x * 5x) + 8 + -3 = 6x + -3(6 + -1x) + 8x (50x + -10x2) + 8 + -3 = 6x + -3(6 + -1x) + 8x Reorder the terms: 8 + -3 + 50x + -10x2 = 6x + -3(6 + -1x) + 8x Combine like terms: 8 + -3 = 5 5 + 50x + -10x2 = 6x + -3(6 + -1x) + 8x 5 + 50x + -10x2 = 6x + (6 * -3 + -1x * -3) + 8x 5 + 50x + -10x2 = 6x + (-18 + 3x) + 8x Reorder the terms: 5 + 50x + -10x2 = -18 + 6x + 3x + 8x Combine like terms: 6x + 3x = 9x 5 + 50x + -10x2 = -18 + 9x + 8x Combine like terms: 9x + 8x = 17x 5 + 50x + -10x2 = -18 + 17x Solving 5 + 50x + -10x2 = -18 + 17x Solving for variable 'x'. Reorder the terms: 5 + 18 + 50x + -17x + -10x2 = -18 + 17x + 18 + -17x Combine like terms: 5 + 18 = 23 23 + 50x + -17x + -10x2 = -18 + 17x + 18 + -17x Combine like terms: 50x + -17x = 33x 23 + 33x + -10x2 = -18 + 17x + 18 + -17x Reorder the terms: 23 + 33x + -10x2 = -18 + 18 + 17x + -17x Combine like terms: -18 + 18 = 0 23 + 33x + -10x2 = 0 + 17x + -17x 23 + 33x + -10x2 = 17x + -17x Combine like terms: 17x + -17x = 0 23 + 33x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -2.3 + -3.3x + x2 = 0.0 Move the constant term to the right: Add '2.3' to each side of the equation. -2.3 + -3.3x + 2.3 + x2 = 0.0 + 2.3 Reorder the terms: -2.3 + 2.3 + -3.3x + x2 = 0.0 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + -3.3x + x2 = 0.0 + 2.3 -3.3x + x2 = 0.0 + 2.3 Combine like terms: 0.0 + 2.3 = 2.3 -3.3x + x2 = 2.3 The x term is -3.3x. Take half its coefficient (-1.65). Square it (2.7225) and add it to both sides. Add '2.7225' to each side of the equation. -3.3x + 2.7225 + x2 = 2.3 + 2.7225 Reorder the terms: 2.7225 + -3.3x + x2 = 2.3 + 2.7225 Combine like terms: 2.3 + 2.7225 = 5.0225 2.7225 + -3.3x + x2 = 5.0225 Factor a perfect square on the left side: (x + -1.65)(x + -1.65) = 5.0225 Calculate the square root of the right side: 2.241093483 Break this problem into two subproblems by setting (x + -1.65) equal to 2.241093483 and -2.241093483.Subproblem 1
x + -1.65 = 2.241093483 Simplifying x + -1.65 = 2.241093483 Reorder the terms: -1.65 + x = 2.241093483 Solving -1.65 + x = 2.241093483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.65' to each side of the equation. -1.65 + 1.65 + x = 2.241093483 + 1.65 Combine like terms: -1.65 + 1.65 = 0.00 0.00 + x = 2.241093483 + 1.65 x = 2.241093483 + 1.65 Combine like terms: 2.241093483 + 1.65 = 3.891093483 x = 3.891093483 Simplifying x = 3.891093483Subproblem 2
x + -1.65 = -2.241093483 Simplifying x + -1.65 = -2.241093483 Reorder the terms: -1.65 + x = -2.241093483 Solving -1.65 + x = -2.241093483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.65' to each side of the equation. -1.65 + 1.65 + x = -2.241093483 + 1.65 Combine like terms: -1.65 + 1.65 = 0.00 0.00 + x = -2.241093483 + 1.65 x = -2.241093483 + 1.65 Combine like terms: -2.241093483 + 1.65 = -0.591093483 x = -0.591093483 Simplifying x = -0.591093483Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.891093483, -0.591093483}
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