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Simplifying -5x(2x + -9) = 2(x + -8) + -11 Reorder the terms: -5x(-9 + 2x) = 2(x + -8) + -11 (-9 * -5x + 2x * -5x) = 2(x + -8) + -11 (45x + -10x2) = 2(x + -8) + -11 Reorder the terms: 45x + -10x2 = 2(-8 + x) + -11 45x + -10x2 = (-8 * 2 + x * 2) + -11 45x + -10x2 = (-16 + 2x) + -11 Reorder the terms: 45x + -10x2 = -16 + -11 + 2x Combine like terms: -16 + -11 = -27 45x + -10x2 = -27 + 2x Solving 45x + -10x2 = -27 + 2x Solving for variable 'x'. Reorder the terms: 27 + 45x + -2x + -10x2 = -27 + 2x + 27 + -2x Combine like terms: 45x + -2x = 43x 27 + 43x + -10x2 = -27 + 2x + 27 + -2x Reorder the terms: 27 + 43x + -10x2 = -27 + 27 + 2x + -2x Combine like terms: -27 + 27 = 0 27 + 43x + -10x2 = 0 + 2x + -2x 27 + 43x + -10x2 = 2x + -2x Combine like terms: 2x + -2x = 0 27 + 43x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -2.7 + -4.3x + x2 = 0.0 Move the constant term to the right: Add '2.7' to each side of the equation. -2.7 + -4.3x + 2.7 + x2 = 0.0 + 2.7 Reorder the terms: -2.7 + 2.7 + -4.3x + x2 = 0.0 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + -4.3x + x2 = 0.0 + 2.7 -4.3x + x2 = 0.0 + 2.7 Combine like terms: 0.0 + 2.7 = 2.7 -4.3x + x2 = 2.7 The x term is -4.3x. Take half its coefficient (-2.15). Square it (4.6225) and add it to both sides. Add '4.6225' to each side of the equation. -4.3x + 4.6225 + x2 = 2.7 + 4.6225 Reorder the terms: 4.6225 + -4.3x + x2 = 2.7 + 4.6225 Combine like terms: 2.7 + 4.6225 = 7.3225 4.6225 + -4.3x + x2 = 7.3225 Factor a perfect square on the left side: (x + -2.15)(x + -2.15) = 7.3225 Calculate the square root of the right side: 2.706011826 Break this problem into two subproblems by setting (x + -2.15) equal to 2.706011826 and -2.706011826.Subproblem 1
x + -2.15 = 2.706011826 Simplifying x + -2.15 = 2.706011826 Reorder the terms: -2.15 + x = 2.706011826 Solving -2.15 + x = 2.706011826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.15' to each side of the equation. -2.15 + 2.15 + x = 2.706011826 + 2.15 Combine like terms: -2.15 + 2.15 = 0.00 0.00 + x = 2.706011826 + 2.15 x = 2.706011826 + 2.15 Combine like terms: 2.706011826 + 2.15 = 4.856011826 x = 4.856011826 Simplifying x = 4.856011826Subproblem 2
x + -2.15 = -2.706011826 Simplifying x + -2.15 = -2.706011826 Reorder the terms: -2.15 + x = -2.706011826 Solving -2.15 + x = -2.706011826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.15' to each side of the equation. -2.15 + 2.15 + x = -2.706011826 + 2.15 Combine like terms: -2.15 + 2.15 = 0.00 0.00 + x = -2.706011826 + 2.15 x = -2.706011826 + 2.15 Combine like terms: -2.706011826 + 2.15 = -0.556011826 x = -0.556011826 Simplifying x = -0.556011826Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.856011826, -0.556011826}
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