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Simplifying 6050 = -10x2 + 335x + 3700 Reorder the terms: 6050 = 3700 + 335x + -10x2 Solving 6050 = 3700 + 335x + -10x2 Solving for variable 'x'. Combine like terms: 6050 + -3700 = 2350 2350 + -335x + 10x2 = 3700 + 335x + -10x2 + -3700 + -335x + 10x2 Reorder the terms: 2350 + -335x + 10x2 = 3700 + -3700 + 335x + -335x + -10x2 + 10x2 Combine like terms: 3700 + -3700 = 0 2350 + -335x + 10x2 = 0 + 335x + -335x + -10x2 + 10x2 2350 + -335x + 10x2 = 335x + -335x + -10x2 + 10x2 Combine like terms: 335x + -335x = 0 2350 + -335x + 10x2 = 0 + -10x2 + 10x2 2350 + -335x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 2350 + -335x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(470 + -67x + 2x2) = 0 Factor a trinomial. 5((10 + -1x)(47 + -2x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Subproblem 2
Set the factor '(47 + -2x)' equal to zero and attempt to solve: Simplifying 47 + -2x = 0 Solving 47 + -2x = 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 + -2x = 0 + -47 Combine like terms: 47 + -47 = 0 0 + -2x = 0 + -47 -2x = 0 + -47 Combine like terms: 0 + -47 = -47 -2x = -47 Divide each side by '-2'. x = 23.5 Simplifying x = 23.5Solution
x = {10, 23.5}
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