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Simplifying 10x2 + -12x + -28 = 0 Reorder the terms: -28 + -12x + 10x2 = 0 Solving -28 + -12x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + -6x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + -6x + 5x2)' equal to zero and attempt to solve: Simplifying -14 + -6x + 5x2 = 0 Solving -14 + -6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + -1.2x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -1.2x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -1.2x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -1.2x + x2 = 0 + 2.8 -1.2x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -1.2x + x2 = 2.8 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 2.8 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 2.8 + 0.36 Combine like terms: 2.8 + 0.36 = 3.16 0.36 + -1.2x + x2 = 3.16 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 3.16 Calculate the square root of the right side: 1.777638883 Break this problem into two subproblems by setting (x + -0.6) equal to 1.777638883 and -1.777638883.Subproblem 1
x + -0.6 = 1.777638883 Simplifying x + -0.6 = 1.777638883 Reorder the terms: -0.6 + x = 1.777638883 Solving -0.6 + x = 1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.777638883 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.777638883 + 0.6 x = 1.777638883 + 0.6 Combine like terms: 1.777638883 + 0.6 = 2.377638883 x = 2.377638883 Simplifying x = 2.377638883Subproblem 2
x + -0.6 = -1.777638883 Simplifying x + -0.6 = -1.777638883 Reorder the terms: -0.6 + x = -1.777638883 Solving -0.6 + x = -1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.777638883 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.777638883 + 0.6 x = -1.777638883 + 0.6 Combine like terms: -1.777638883 + 0.6 = -1.177638883 x = -1.177638883 Simplifying x = -1.177638883Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.377638883, -1.177638883}Solution
x = {2.377638883, -1.177638883}
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