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Simplifying 4x(x + 6) + -7(5 + 8x) = 0 Reorder the terms: 4x(6 + x) + -7(5 + 8x) = 0 (6 * 4x + x * 4x) + -7(5 + 8x) = 0 (24x + 4x2) + -7(5 + 8x) = 0 24x + 4x2 + (5 * -7 + 8x * -7) = 0 24x + 4x2 + (-35 + -56x) = 0 Reorder the terms: -35 + 24x + -56x + 4x2 = 0 Combine like terms: 24x + -56x = -32x -35 + -32x + 4x2 = 0 Solving -35 + -32x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + -8x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -8x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -8x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -8x + x2 = 0 + 8.75 -8x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -8x + x2 = 8.75 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 8.75 + 16 Reorder the terms: 16 + -8x + x2 = 8.75 + 16 Combine like terms: 8.75 + 16 = 24.75 16 + -8x + x2 = 24.75 Factor a perfect square on the left side: (x + -4)(x + -4) = 24.75 Calculate the square root of the right side: 4.974937186 Break this problem into two subproblems by setting (x + -4) equal to 4.974937186 and -4.974937186.Subproblem 1
x + -4 = 4.974937186 Simplifying x + -4 = 4.974937186 Reorder the terms: -4 + x = 4.974937186 Solving -4 + x = 4.974937186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.974937186 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.974937186 + 4 x = 4.974937186 + 4 Combine like terms: 4.974937186 + 4 = 8.974937186 x = 8.974937186 Simplifying x = 8.974937186Subproblem 2
x + -4 = -4.974937186 Simplifying x + -4 = -4.974937186 Reorder the terms: -4 + x = -4.974937186 Solving -4 + x = -4.974937186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.974937186 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.974937186 + 4 x = -4.974937186 + 4 Combine like terms: -4.974937186 + 4 = -0.974937186 x = -0.974937186 Simplifying x = -0.974937186Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.974937186, -0.974937186}
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