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Simplifying 0 = 10(3x2 + 62x + -200) Reorder the terms: 0 = 10(-200 + 62x + 3x2) 0 = (-200 * 10 + 62x * 10 + 3x2 * 10) 0 = (-2000 + 620x + 30x2) Solving 0 = -2000 + 620x + 30x2 Solving for variable 'x'. Combine like terms: 0 + 2000 = 2000 2000 + -620x + -30x2 = -2000 + 620x + 30x2 + 2000 + -620x + -30x2 Reorder the terms: 2000 + -620x + -30x2 = -2000 + 2000 + 620x + -620x + 30x2 + -30x2 Combine like terms: -2000 + 2000 = 0 2000 + -620x + -30x2 = 0 + 620x + -620x + 30x2 + -30x2 2000 + -620x + -30x2 = 620x + -620x + 30x2 + -30x2 Combine like terms: 620x + -620x = 0 2000 + -620x + -30x2 = 0 + 30x2 + -30x2 2000 + -620x + -30x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 2000 + -620x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(200 + -62x + -3x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(200 + -62x + -3x2)' equal to zero and attempt to solve: Simplifying 200 + -62x + -3x2 = 0 Solving 200 + -62x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -66.66666667 + 20.66666667x + x2 = 0 Move the constant term to the right: Add '66.66666667' to each side of the equation. -66.66666667 + 20.66666667x + 66.66666667 + x2 = 0 + 66.66666667 Reorder the terms: -66.66666667 + 66.66666667 + 20.66666667x + x2 = 0 + 66.66666667 Combine like terms: -66.66666667 + 66.66666667 = 0.00000000 0.00000000 + 20.66666667x + x2 = 0 + 66.66666667 20.66666667x + x2 = 0 + 66.66666667 Combine like terms: 0 + 66.66666667 = 66.66666667 20.66666667x + x2 = 66.66666667 The x term is 20.66666667x. Take half its coefficient (10.33333334). Square it (106.7777779) and add it to both sides. Add '106.7777779' to each side of the equation. 20.66666667x + 106.7777779 + x2 = 66.66666667 + 106.7777779 Reorder the terms: 106.7777779 + 20.66666667x + x2 = 66.66666667 + 106.7777779 Combine like terms: 66.66666667 + 106.7777779 = 173.44444457 106.7777779 + 20.66666667x + x2 = 173.44444457 Factor a perfect square on the left side: (x + 10.33333334)(x + 10.33333334) = 173.44444457 Calculate the square root of the right side: 13.169830848 Break this problem into two subproblems by setting (x + 10.33333334) equal to 13.169830848 and -13.169830848.Subproblem 1
x + 10.33333334 = 13.169830848 Simplifying x + 10.33333334 = 13.169830848 Reorder the terms: 10.33333334 + x = 13.169830848 Solving 10.33333334 + x = 13.169830848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.33333334' to each side of the equation. 10.33333334 + -10.33333334 + x = 13.169830848 + -10.33333334 Combine like terms: 10.33333334 + -10.33333334 = 0.00000000 0.00000000 + x = 13.169830848 + -10.33333334 x = 13.169830848 + -10.33333334 Combine like terms: 13.169830848 + -10.33333334 = 2.836497508 x = 2.836497508 Simplifying x = 2.836497508Subproblem 2
x + 10.33333334 = -13.169830848 Simplifying x + 10.33333334 = -13.169830848 Reorder the terms: 10.33333334 + x = -13.169830848 Solving 10.33333334 + x = -13.169830848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.33333334' to each side of the equation. 10.33333334 + -10.33333334 + x = -13.169830848 + -10.33333334 Combine like terms: 10.33333334 + -10.33333334 = 0.00000000 0.00000000 + x = -13.169830848 + -10.33333334 x = -13.169830848 + -10.33333334 Combine like terms: -13.169830848 + -10.33333334 = -23.503164188 x = -23.503164188 Simplifying x = -23.503164188Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.836497508, -23.503164188}Solution
x = {2.836497508, -23.503164188}
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