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Simplifying 4x(5x + 7) + 2(x + 6) = 28 Reorder the terms: 4x(7 + 5x) + 2(x + 6) = 28 (7 * 4x + 5x * 4x) + 2(x + 6) = 28 (28x + 20x2) + 2(x + 6) = 28 Reorder the terms: 28x + 20x2 + 2(6 + x) = 28 28x + 20x2 + (6 * 2 + x * 2) = 28 28x + 20x2 + (12 + 2x) = 28 Reorder the terms: 12 + 28x + 2x + 20x2 = 28 Combine like terms: 28x + 2x = 30x 12 + 30x + 20x2 = 28 Solving 12 + 30x + 20x2 = 28 Solving for variable 'x'. Reorder the terms: 12 + -28 + 30x + 20x2 = 28 + -28 Combine like terms: 12 + -28 = -16 -16 + 30x + 20x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -16 + 30x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 15x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 15x + 10x2)' equal to zero and attempt to solve: Simplifying -8 + 15x + 10x2 = 0 Solving -8 + 15x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.8 + 1.5x + x2 = 0.0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 1.5x + 0.8 + x2 = 0.0 + 0.8 Reorder the terms: -0.8 + 0.8 + 1.5x + x2 = 0.0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 1.5x + x2 = 0.0 + 0.8 1.5x + x2 = 0.0 + 0.8 Combine like terms: 0.0 + 0.8 = 0.8 1.5x + x2 = 0.8 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 0.8 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 0.8 + 0.5625 Combine like terms: 0.8 + 0.5625 = 1.3625 0.5625 + 1.5x + x2 = 1.3625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 1.3625 Calculate the square root of the right side: 1.167261753 Break this problem into two subproblems by setting (x + 0.75) equal to 1.167261753 and -1.167261753.Subproblem 1
x + 0.75 = 1.167261753 Simplifying x + 0.75 = 1.167261753 Reorder the terms: 0.75 + x = 1.167261753 Solving 0.75 + x = 1.167261753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.167261753 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.167261753 + -0.75 x = 1.167261753 + -0.75 Combine like terms: 1.167261753 + -0.75 = 0.417261753 x = 0.417261753 Simplifying x = 0.417261753Subproblem 2
x + 0.75 = -1.167261753 Simplifying x + 0.75 = -1.167261753 Reorder the terms: 0.75 + x = -1.167261753 Solving 0.75 + x = -1.167261753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.167261753 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.167261753 + -0.75 x = -1.167261753 + -0.75 Combine like terms: -1.167261753 + -0.75 = -1.917261753 x = -1.917261753 Simplifying x = -1.917261753Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.417261753, -1.917261753}Solution
x = {0.417261753, -1.917261753}
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