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Simplifying (6x + -5)(4x + 10) = 175 Reorder the terms: (-5 + 6x)(4x + 10) = 175 Reorder the terms: (-5 + 6x)(10 + 4x) = 175 Multiply (-5 + 6x) * (10 + 4x) (-5(10 + 4x) + 6x * (10 + 4x)) = 175 ((10 * -5 + 4x * -5) + 6x * (10 + 4x)) = 175 ((-50 + -20x) + 6x * (10 + 4x)) = 175 (-50 + -20x + (10 * 6x + 4x * 6x)) = 175 (-50 + -20x + (60x + 24x2)) = 175 Combine like terms: -20x + 60x = 40x (-50 + 40x + 24x2) = 175 Solving -50 + 40x + 24x2 = 175 Solving for variable 'x'. Reorder the terms: -50 + -175 + 40x + 24x2 = 175 + -175 Combine like terms: -50 + -175 = -225 -225 + 40x + 24x2 = 175 + -175 Combine like terms: 175 + -175 = 0 -225 + 40x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -9.375 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + 1.666666667x + 9.375 + x2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + 1.666666667x + x2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + 1.666666667x + x2 = 0 + 9.375 1.666666667x + x2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 1.666666667x + x2 = 9.375 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 9.375 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 9.375 + 0.6944444447 Combine like terms: 9.375 + 0.6944444447 = 10.0694444447 0.6944444447 + 1.666666667x + x2 = 10.0694444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 10.0694444447 Calculate the square root of the right side: 3.173238794 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 3.173238794 and -3.173238794.Subproblem 1
x + 0.8333333335 = 3.173238794 Simplifying x + 0.8333333335 = 3.173238794 Reorder the terms: 0.8333333335 + x = 3.173238794 Solving 0.8333333335 + x = 3.173238794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 3.173238794 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 3.173238794 + -0.8333333335 x = 3.173238794 + -0.8333333335 Combine like terms: 3.173238794 + -0.8333333335 = 2.3399054605 x = 2.3399054605 Simplifying x = 2.3399054605Subproblem 2
x + 0.8333333335 = -3.173238794 Simplifying x + 0.8333333335 = -3.173238794 Reorder the terms: 0.8333333335 + x = -3.173238794 Solving 0.8333333335 + x = -3.173238794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -3.173238794 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -3.173238794 + -0.8333333335 x = -3.173238794 + -0.8333333335 Combine like terms: -3.173238794 + -0.8333333335 = -4.0065721275 x = -4.0065721275 Simplifying x = -4.0065721275Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3399054605, -4.0065721275}
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