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Simplifying H(0) = -20x2 + 44x + -21 Reorder the terms for easier multiplication: 0H = -20x2 + 44x + -21 Anything times zero is zero. 0H = -20x2 + 44x + -21 Reorder the terms: 0 = -21 + 44x + -20x2 Solving 0 = -21 + 44x + -20x2 Solving for variable 'x'. Combine like terms: 0 + 21 = 21 21 + -44x + 20x2 = -21 + 44x + -20x2 + 21 + -44x + 20x2 Reorder the terms: 21 + -44x + 20x2 = -21 + 21 + 44x + -44x + -20x2 + 20x2 Combine like terms: -21 + 21 = 0 21 + -44x + 20x2 = 0 + 44x + -44x + -20x2 + 20x2 21 + -44x + 20x2 = 44x + -44x + -20x2 + 20x2 Combine like terms: 44x + -44x = 0 21 + -44x + 20x2 = 0 + -20x2 + 20x2 21 + -44x + 20x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 21 + -44x + 20x2 = 0 Factor a trinomial. (7 + -10x)(3 + -2x) = 0Subproblem 1
Set the factor '(7 + -10x)' equal to zero and attempt to solve: Simplifying 7 + -10x = 0 Solving 7 + -10x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -10x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -10x = 0 + -7 -10x = 0 + -7 Combine like terms: 0 + -7 = -7 -10x = -7 Divide each side by '-10'. x = 0.7 Simplifying x = 0.7Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {0.7, 1.5}
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