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Simplifying (4x3 + -6x2 + -24x) * 10 + -1x = 0 Reorder the terms: (-24x + -6x2 + 4x3) * 10 + -1x = 0 Reorder the terms for easier multiplication: 10(-24x + -6x2 + 4x3) + -1x = 0 (-24x * 10 + -6x2 * 10 + 4x3 * 10) + -1x = 0 (-240x + -60x2 + 40x3) + -1x = 0 Reorder the terms: -240x + -1x + -60x2 + 40x3 = 0 Combine like terms: -240x + -1x = -241x -241x + -60x2 + 40x3 = 0 Solving -241x + -60x2 + 40x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-241 + -60x + 40x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-241 + -60x + 40x2)' equal to zero and attempt to solve: Simplifying -241 + -60x + 40x2 = 0 Solving -241 + -60x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -6.025 + -1.5x + x2 = 0.0 Move the constant term to the right: Add '6.025' to each side of the equation. -6.025 + -1.5x + 6.025 + x2 = 0.0 + 6.025 Reorder the terms: -6.025 + 6.025 + -1.5x + x2 = 0.0 + 6.025 Combine like terms: -6.025 + 6.025 = 0.000 0.000 + -1.5x + x2 = 0.0 + 6.025 -1.5x + x2 = 0.0 + 6.025 Combine like terms: 0.0 + 6.025 = 6.025 -1.5x + x2 = 6.025 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 = 6.025 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 6.025 + 0.5625 Combine like terms: 6.025 + 0.5625 = 6.5875 0.5625 + -1.5x + x2 = 6.5875 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 6.5875 Calculate the square root of the right side: 2.566612554 Break this problem into two subproblems by setting (x + -0.75) equal to 2.566612554 and -2.566612554.Subproblem 1
x + -0.75 = 2.566612554 Simplifying x + -0.75 = 2.566612554 Reorder the terms: -0.75 + x = 2.566612554 Solving -0.75 + x = 2.566612554 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 = 2.566612554 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.566612554 + 0.75 x = 2.566612554 + 0.75 Combine like terms: 2.566612554 + 0.75 = 3.316612554 x = 3.316612554 Simplifying x = 3.316612554Subproblem 2
x + -0.75 = -2.566612554 Simplifying x + -0.75 = -2.566612554 Reorder the terms: -0.75 + x = -2.566612554 Solving -0.75 + x = -2.566612554 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 = -2.566612554 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.566612554 + 0.75 x = -2.566612554 + 0.75 Combine like terms: -2.566612554 + 0.75 = -1.816612554 x = -1.816612554 Simplifying x = -1.816612554Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.316612554, -1.816612554}Solution
x = {0, 3.316612554, -1.816612554}
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