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Simplifying 6x2 + 6x + -870 = 0 Reorder the terms: -870 + 6x + 6x2 = 0 Solving -870 + 6x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-145 + x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-145 + x + x2)' equal to zero and attempt to solve: Simplifying -145 + x + x2 = 0 Solving -145 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '145' to each side of the equation. -145 + x + 145 + x2 = 0 + 145 Reorder the terms: -145 + 145 + x + x2 = 0 + 145 Combine like terms: -145 + 145 = 0 0 + x + x2 = 0 + 145 x + x2 = 0 + 145 Combine like terms: 0 + 145 = 145 x + x2 = 145 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 145 + 0.25 Reorder the terms: 0.25 + x + x2 = 145 + 0.25 Combine like terms: 145 + 0.25 = 145.25 0.25 + x + x2 = 145.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 145.25 Calculate the square root of the right side: 12.051970793 Break this problem into two subproblems by setting (x + 0.5) equal to 12.051970793 and -12.051970793.Subproblem 1
x + 0.5 = 12.051970793 Simplifying x + 0.5 = 12.051970793 Reorder the terms: 0.5 + x = 12.051970793 Solving 0.5 + x = 12.051970793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 12.051970793 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.051970793 + -0.5 x = 12.051970793 + -0.5 Combine like terms: 12.051970793 + -0.5 = 11.551970793 x = 11.551970793 Simplifying x = 11.551970793Subproblem 2
x + 0.5 = -12.051970793 Simplifying x + 0.5 = -12.051970793 Reorder the terms: 0.5 + x = -12.051970793 Solving 0.5 + x = -12.051970793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -12.051970793 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.051970793 + -0.5 x = -12.051970793 + -0.5 Combine like terms: -12.051970793 + -0.5 = -12.551970793 x = -12.551970793 Simplifying x = -12.551970793Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.551970793, -12.551970793}Solution
x = {11.551970793, -12.551970793}
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