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Simplifying 10000 = 4x2 + 24x + 36 Reorder the terms: 10000 = 36 + 24x + 4x2 Solving 10000 = 36 + 24x + 4x2 Solving for variable 'x'. Combine like terms: 10000 + -36 = 9964 9964 + -24x + -4x2 = 36 + 24x + 4x2 + -36 + -24x + -4x2 Reorder the terms: 9964 + -24x + -4x2 = 36 + -36 + 24x + -24x + 4x2 + -4x2 Combine like terms: 36 + -36 = 0 9964 + -24x + -4x2 = 0 + 24x + -24x + 4x2 + -4x2 9964 + -24x + -4x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 9964 + -24x + -4x2 = 0 + 4x2 + -4x2 9964 + -24x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 9964 + -24x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(2491 + -6x + -1x2) = 0 Factor a trinomial. 4((47 + -1x)(53 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(47 + -1x)' equal to zero and attempt to solve: Simplifying 47 + -1x = 0 Solving 47 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-47' to each side of the equation. 47 + -47 + -1x = 0 + -47 Combine like terms: 47 + -47 = 0 0 + -1x = 0 + -47 -1x = 0 + -47 Combine like terms: 0 + -47 = -47 -1x = -47 Divide each side by '-1'. x = 47 Simplifying x = 47Subproblem 2
Set the factor '(53 + x)' equal to zero and attempt to solve: Simplifying 53 + x = 0 Solving 53 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-53' to each side of the equation. 53 + -53 + x = 0 + -53 Combine like terms: 53 + -53 = 0 0 + x = 0 + -53 x = 0 + -53 Combine like terms: 0 + -53 = -53 x = -53 Simplifying x = -53Solution
x = {47, -53}
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