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Simplifying (6 + -24x) + -1(8x2 + 2) = 7 Remove parenthesis around (6 + -24x) 6 + -24x + -1(8x2 + 2) = 7 Reorder the terms: 6 + -24x + -1(2 + 8x2) = 7 6 + -24x + (2 * -1 + 8x2 * -1) = 7 6 + -24x + (-2 + -8x2) = 7 Reorder the terms: 6 + -2 + -24x + -8x2 = 7 Combine like terms: 6 + -2 = 4 4 + -24x + -8x2 = 7 Solving 4 + -24x + -8x2 = 7 Solving for variable 'x'. Reorder the terms: 4 + -7 + -24x + -8x2 = 7 + -7 Combine like terms: 4 + -7 = -3 -3 + -24x + -8x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -3 + -24x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 24x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 24x + 8x2)' equal to zero and attempt to solve: Simplifying 3 + 24x + 8x2 = 0 Solving 3 + 24x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 3x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 3x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 3x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 3x + x2 = 0 + -0.375 3x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 3x + x2 = -0.375 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -0.375 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -0.375 + 2.25 Combine like terms: -0.375 + 2.25 = 1.875 2.25 + 3x + x2 = 1.875 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.875 Calculate the square root of the right side: 1.369306394 Break this problem into two subproblems by setting (x + 1.5) equal to 1.369306394 and -1.369306394.Subproblem 1
x + 1.5 = 1.369306394 Simplifying x + 1.5 = 1.369306394 Reorder the terms: 1.5 + x = 1.369306394 Solving 1.5 + x = 1.369306394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.369306394 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.369306394 + -1.5 x = 1.369306394 + -1.5 Combine like terms: 1.369306394 + -1.5 = -0.130693606 x = -0.130693606 Simplifying x = -0.130693606Subproblem 2
x + 1.5 = -1.369306394 Simplifying x + 1.5 = -1.369306394 Reorder the terms: 1.5 + x = -1.369306394 Solving 1.5 + x = -1.369306394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.369306394 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.369306394 + -1.5 x = -1.369306394 + -1.5 Combine like terms: -1.369306394 + -1.5 = -2.869306394 x = -2.869306394 Simplifying x = -2.869306394Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.130693606, -2.869306394}Solution
x = {-0.130693606, -2.869306394}
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