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Simplifying 6(3x2 + 5x + -2) + 3x2 + -4 = 0 Reorder the terms: 6(-2 + 5x + 3x2) + 3x2 + -4 = 0 (-2 * 6 + 5x * 6 + 3x2 * 6) + 3x2 + -4 = 0 (-12 + 30x + 18x2) + 3x2 + -4 = 0 Reorder the terms: -12 + -4 + 30x + 18x2 + 3x2 = 0 Combine like terms: -12 + -4 = -16 -16 + 30x + 18x2 + 3x2 = 0 Combine like terms: 18x2 + 3x2 = 21x2 -16 + 30x + 21x2 = 0 Solving -16 + 30x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.7619047619 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '0.7619047619' to each side of the equation. -0.7619047619 + 1.428571429x + 0.7619047619 + x2 = 0 + 0.7619047619 Reorder the terms: -0.7619047619 + 0.7619047619 + 1.428571429x + x2 = 0 + 0.7619047619 Combine like terms: -0.7619047619 + 0.7619047619 = 0.0000000000 0.0000000000 + 1.428571429x + x2 = 0 + 0.7619047619 1.428571429x + x2 = 0 + 0.7619047619 Combine like terms: 0 + 0.7619047619 = 0.7619047619 1.428571429x + x2 = 0.7619047619 The x term is 1.428571429x. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429x + 0.5102040819 + x2 = 0.7619047619 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 0.7619047619 + 0.5102040819 Combine like terms: 0.7619047619 + 0.5102040819 = 1.2721088438 0.5102040819 + 1.428571429x + x2 = 1.2721088438 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 1.2721088438 Calculate the square root of the right side: 1.127878027 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 1.127878027 and -1.127878027.Subproblem 1
x + 0.7142857145 = 1.127878027 Simplifying x + 0.7142857145 = 1.127878027 Reorder the terms: 0.7142857145 + x = 1.127878027 Solving 0.7142857145 + x = 1.127878027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 1.127878027 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 1.127878027 + -0.7142857145 x = 1.127878027 + -0.7142857145 Combine like terms: 1.127878027 + -0.7142857145 = 0.4135923125 x = 0.4135923125 Simplifying x = 0.4135923125Subproblem 2
x + 0.7142857145 = -1.127878027 Simplifying x + 0.7142857145 = -1.127878027 Reorder the terms: 0.7142857145 + x = -1.127878027 Solving 0.7142857145 + x = -1.127878027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -1.127878027 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -1.127878027 + -0.7142857145 x = -1.127878027 + -0.7142857145 Combine like terms: -1.127878027 + -0.7142857145 = -1.8421637415 x = -1.8421637415 Simplifying x = -1.8421637415Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4135923125, -1.8421637415}
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