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Simplifying 0 = 6x2 + -310x + -600 Reorder the terms: 0 = -600 + -310x + 6x2 Solving 0 = -600 + -310x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 600 = 600 600 + 310x + -6x2 = -600 + -310x + 6x2 + 600 + 310x + -6x2 Reorder the terms: 600 + 310x + -6x2 = -600 + 600 + -310x + 310x + 6x2 + -6x2 Combine like terms: -600 + 600 = 0 600 + 310x + -6x2 = 0 + -310x + 310x + 6x2 + -6x2 600 + 310x + -6x2 = -310x + 310x + 6x2 + -6x2 Combine like terms: -310x + 310x = 0 600 + 310x + -6x2 = 0 + 6x2 + -6x2 600 + 310x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 600 + 310x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(300 + 155x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(300 + 155x + -3x2)' equal to zero and attempt to solve: Simplifying 300 + 155x + -3x2 = 0 Solving 300 + 155x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -100 + -51.66666667x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -51.66666667x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -51.66666667x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -51.66666667x + x2 = 0 + 100 -51.66666667x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -51.66666667x + x2 = 100 The x term is -51.66666667x. Take half its coefficient (-25.83333334). Square it (667.3611115) and add it to both sides. Add '667.3611115' to each side of the equation. -51.66666667x + 667.3611115 + x2 = 100 + 667.3611115 Reorder the terms: 667.3611115 + -51.66666667x + x2 = 100 + 667.3611115 Combine like terms: 100 + 667.3611115 = 767.3611115 667.3611115 + -51.66666667x + x2 = 767.3611115 Factor a perfect square on the left side: (x + -25.83333334)(x + -25.83333334) = 767.3611115 Calculate the square root of the right side: 27.701283571 Break this problem into two subproblems by setting (x + -25.83333334) equal to 27.701283571 and -27.701283571.Subproblem 1
x + -25.83333334 = 27.701283571 Simplifying x + -25.83333334 = 27.701283571 Reorder the terms: -25.83333334 + x = 27.701283571 Solving -25.83333334 + x = 27.701283571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.83333334' to each side of the equation. -25.83333334 + 25.83333334 + x = 27.701283571 + 25.83333334 Combine like terms: -25.83333334 + 25.83333334 = 0.00000000 0.00000000 + x = 27.701283571 + 25.83333334 x = 27.701283571 + 25.83333334 Combine like terms: 27.701283571 + 25.83333334 = 53.534616911 x = 53.534616911 Simplifying x = 53.534616911Subproblem 2
x + -25.83333334 = -27.701283571 Simplifying x + -25.83333334 = -27.701283571 Reorder the terms: -25.83333334 + x = -27.701283571 Solving -25.83333334 + x = -27.701283571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.83333334' to each side of the equation. -25.83333334 + 25.83333334 + x = -27.701283571 + 25.83333334 Combine like terms: -25.83333334 + 25.83333334 = 0.00000000 0.00000000 + x = -27.701283571 + 25.83333334 x = -27.701283571 + 25.83333334 Combine like terms: -27.701283571 + 25.83333334 = -1.867950231 x = -1.867950231 Simplifying x = -1.867950231Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.534616911, -1.867950231}Solution
x = {53.534616911, -1.867950231}
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