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Simplifying 27 + -4x = -5x(4x + 5) + -5(-8 + -3x) Reorder the terms: 27 + -4x = -5x(5 + 4x) + -5(-8 + -3x) 27 + -4x = (5 * -5x + 4x * -5x) + -5(-8 + -3x) 27 + -4x = (-25x + -20x2) + -5(-8 + -3x) 27 + -4x = -25x + -20x2 + (-8 * -5 + -3x * -5) 27 + -4x = -25x + -20x2 + (40 + 15x) Reorder the terms: 27 + -4x = 40 + -25x + 15x + -20x2 Combine like terms: -25x + 15x = -10x 27 + -4x = 40 + -10x + -20x2 Solving 27 + -4x = 40 + -10x + -20x2 Solving for variable 'x'. Reorder the terms: 27 + -40 + -4x + 10x + 20x2 = 40 + -10x + -20x2 + -40 + 10x + 20x2 Combine like terms: 27 + -40 = -13 -13 + -4x + 10x + 20x2 = 40 + -10x + -20x2 + -40 + 10x + 20x2 Combine like terms: -4x + 10x = 6x -13 + 6x + 20x2 = 40 + -10x + -20x2 + -40 + 10x + 20x2 Reorder the terms: -13 + 6x + 20x2 = 40 + -40 + -10x + 10x + -20x2 + 20x2 Combine like terms: 40 + -40 = 0 -13 + 6x + 20x2 = 0 + -10x + 10x + -20x2 + 20x2 -13 + 6x + 20x2 = -10x + 10x + -20x2 + 20x2 Combine like terms: -10x + 10x = 0 -13 + 6x + 20x2 = 0 + -20x2 + 20x2 -13 + 6x + 20x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 -13 + 6x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.65 + 0.3x + x2 = 0 Move the constant term to the right: Add '0.65' to each side of the equation. -0.65 + 0.3x + 0.65 + x2 = 0 + 0.65 Reorder the terms: -0.65 + 0.65 + 0.3x + x2 = 0 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + 0.3x + x2 = 0 + 0.65 0.3x + x2 = 0 + 0.65 Combine like terms: 0 + 0.65 = 0.65 0.3x + x2 = 0.65 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 0.65 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 0.65 + 0.0225 Combine like terms: 0.65 + 0.0225 = 0.6725 0.0225 + 0.3x + x2 = 0.6725 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 0.6725 Calculate the square root of the right side: 0.820060973 Break this problem into two subproblems by setting (x + 0.15) equal to 0.820060973 and -0.820060973.Subproblem 1
x + 0.15 = 0.820060973 Simplifying x + 0.15 = 0.820060973 Reorder the terms: 0.15 + x = 0.820060973 Solving 0.15 + x = 0.820060973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 0.820060973 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.820060973 + -0.15 x = 0.820060973 + -0.15 Combine like terms: 0.820060973 + -0.15 = 0.670060973 x = 0.670060973 Simplifying x = 0.670060973Subproblem 2
x + 0.15 = -0.820060973 Simplifying x + 0.15 = -0.820060973 Reorder the terms: 0.15 + x = -0.820060973 Solving 0.15 + x = -0.820060973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -0.820060973 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.820060973 + -0.15 x = -0.820060973 + -0.15 Combine like terms: -0.820060973 + -0.15 = -0.970060973 x = -0.970060973 Simplifying x = -0.970060973Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.670060973, -0.970060973}
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