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Simplifying 350 + -156x + 12x2 = 0 Solving 350 + -156x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(175 + -78x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(175 + -78x + 6x2)' equal to zero and attempt to solve: Simplifying 175 + -78x + 6x2 = 0 Solving 175 + -78x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 29.16666667 + -13x + x2 = 0 Move the constant term to the right: Add '-29.16666667' to each side of the equation. 29.16666667 + -13x + -29.16666667 + x2 = 0 + -29.16666667 Reorder the terms: 29.16666667 + -29.16666667 + -13x + x2 = 0 + -29.16666667 Combine like terms: 29.16666667 + -29.16666667 = 0.00000000 0.00000000 + -13x + x2 = 0 + -29.16666667 -13x + x2 = 0 + -29.16666667 Combine like terms: 0 + -29.16666667 = -29.16666667 -13x + x2 = -29.16666667 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -29.16666667 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -29.16666667 + 42.25 Combine like terms: -29.16666667 + 42.25 = 13.08333333 42.25 + -13x + x2 = 13.08333333 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 13.08333333 Calculate the square root of the right side: 3.617089069 Break this problem into two subproblems by setting (x + -6.5) equal to 3.617089069 and -3.617089069.Subproblem 1
x + -6.5 = 3.617089069 Simplifying x + -6.5 = 3.617089069 Reorder the terms: -6.5 + x = 3.617089069 Solving -6.5 + x = 3.617089069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 3.617089069 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 3.617089069 + 6.5 x = 3.617089069 + 6.5 Combine like terms: 3.617089069 + 6.5 = 10.117089069 x = 10.117089069 Simplifying x = 10.117089069Subproblem 2
x + -6.5 = -3.617089069 Simplifying x + -6.5 = -3.617089069 Reorder the terms: -6.5 + x = -3.617089069 Solving -6.5 + x = -3.617089069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -3.617089069 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -3.617089069 + 6.5 x = -3.617089069 + 6.5 Combine like terms: -3.617089069 + 6.5 = 2.882910931 x = 2.882910931 Simplifying x = 2.882910931Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.117089069, 2.882910931}Solution
x = {10.117089069, 2.882910931}
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