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Simplifying 12x2 + -8 + 3x + -7x2 + -12 = 0 Reorder the terms: -8 + -12 + 3x + 12x2 + -7x2 = 0 Combine like terms: -8 + -12 = -20 -20 + 3x + 12x2 + -7x2 = 0 Combine like terms: 12x2 + -7x2 = 5x2 -20 + 3x + 5x2 = 0 Solving -20 + 3x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + 0.6x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.6x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.6x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.6x + x2 = 0 + 4 0.6x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.6x + x2 = 4 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 4 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 4 + 0.09 Combine like terms: 4 + 0.09 = 4.09 0.09 + 0.6x + x2 = 4.09 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (x + 0.3) equal to 2.022374842 and -2.022374842.Subproblem 1
x + 0.3 = 2.022374842 Simplifying x + 0.3 = 2.022374842 Reorder the terms: 0.3 + x = 2.022374842 Solving 0.3 + x = 2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 2.022374842 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 2.022374842 + -0.3 x = 2.022374842 + -0.3 Combine like terms: 2.022374842 + -0.3 = 1.722374842 x = 1.722374842 Simplifying x = 1.722374842Subproblem 2
x + 0.3 = -2.022374842 Simplifying x + 0.3 = -2.022374842 Reorder the terms: 0.3 + x = -2.022374842 Solving 0.3 + x = -2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -2.022374842 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -2.022374842 + -0.3 x = -2.022374842 + -0.3 Combine like terms: -2.022374842 + -0.3 = -2.322374842 x = -2.322374842 Simplifying x = -2.322374842Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.722374842, -2.322374842}
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