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Simplifying 24x2 + 240x + -1x3 = 0 Reorder the terms: 240x + 24x2 + -1x3 = 0 Solving 240x + 24x2 + -1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(240 + 24x + -1x2) = 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 '(240 + 24x + -1x2)' equal to zero and attempt to solve: Simplifying 240 + 24x + -1x2 = 0 Solving 240 + 24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -240 + -24x + x2 = 0 Move the constant term to the right: Add '240' to each side of the equation. -240 + -24x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + -24x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + -24x + x2 = 0 + 240 -24x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 -24x + x2 = 240 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 240 + 144 Reorder the terms: 144 + -24x + x2 = 240 + 144 Combine like terms: 240 + 144 = 384 144 + -24x + x2 = 384 Factor a perfect square on the left side: (x + -12)(x + -12) = 384 Calculate the square root of the right side: 19.595917942 Break this problem into two subproblems by setting (x + -12) equal to 19.595917942 and -19.595917942.Subproblem 1
x + -12 = 19.595917942 Simplifying x + -12 = 19.595917942 Reorder the terms: -12 + x = 19.595917942 Solving -12 + x = 19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 19.595917942 + 12 Combine like terms: -12 + 12 = 0 0 + x = 19.595917942 + 12 x = 19.595917942 + 12 Combine like terms: 19.595917942 + 12 = 31.595917942 x = 31.595917942 Simplifying x = 31.595917942Subproblem 2
x + -12 = -19.595917942 Simplifying x + -12 = -19.595917942 Reorder the terms: -12 + x = -19.595917942 Solving -12 + x = -19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -19.595917942 + 12 Combine like terms: -12 + 12 = 0 0 + x = -19.595917942 + 12 x = -19.595917942 + 12 Combine like terms: -19.595917942 + 12 = -7.595917942 x = -7.595917942 Simplifying x = -7.595917942Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.595917942, -7.595917942}Solution
x = {0, 31.595917942, -7.595917942}
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