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Simplifying (7x2 + 17x + 13) + -1(12x2 + 10x + 4) = 0 Reorder the terms: (13 + 17x + 7x2) + -1(12x2 + 10x + 4) = 0 Remove parenthesis around (13 + 17x + 7x2) 13 + 17x + 7x2 + -1(12x2 + 10x + 4) = 0 Reorder the terms: 13 + 17x + 7x2 + -1(4 + 10x + 12x2) = 0 13 + 17x + 7x2 + (4 * -1 + 10x * -1 + 12x2 * -1) = 0 13 + 17x + 7x2 + (-4 + -10x + -12x2) = 0 Reorder the terms: 13 + -4 + 17x + -10x + 7x2 + -12x2 = 0 Combine like terms: 13 + -4 = 9 9 + 17x + -10x + 7x2 + -12x2 = 0 Combine like terms: 17x + -10x = 7x 9 + 7x + 7x2 + -12x2 = 0 Combine like terms: 7x2 + -12x2 = -5x2 9 + 7x + -5x2 = 0 Solving 9 + 7x + -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'. -1.8 + -1.4x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -1.4x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -1.4x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -1.4x + x2 = 0 + 1.8 -1.4x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -1.4x + x2 = 1.8 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 1.8 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 1.8 + 0.49 Combine like terms: 1.8 + 0.49 = 2.29 0.49 + -1.4x + x2 = 2.29 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 2.29 Calculate the square root of the right side: 1.513274595 Break this problem into two subproblems by setting (x + -0.7) equal to 1.513274595 and -1.513274595.Subproblem 1
x + -0.7 = 1.513274595 Simplifying x + -0.7 = 1.513274595 Reorder the terms: -0.7 + x = 1.513274595 Solving -0.7 + x = 1.513274595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 1.513274595 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 1.513274595 + 0.7 x = 1.513274595 + 0.7 Combine like terms: 1.513274595 + 0.7 = 2.213274595 x = 2.213274595 Simplifying x = 2.213274595Subproblem 2
x + -0.7 = -1.513274595 Simplifying x + -0.7 = -1.513274595 Reorder the terms: -0.7 + x = -1.513274595 Solving -0.7 + x = -1.513274595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -1.513274595 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -1.513274595 + 0.7 x = -1.513274595 + 0.7 Combine like terms: -1.513274595 + 0.7 = -0.813274595 x = -0.813274595 Simplifying x = -0.813274595Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.213274595, -0.813274595}
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