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Simplifying 14 + -1(5x + -1)(2x + 3) = 0 Reorder the terms: 14 + -1(-1 + 5x)(2x + 3) = 0 Reorder the terms: 14 + -1(-1 + 5x)(3 + 2x) = 0 Multiply (-1 + 5x) * (3 + 2x) 14 + -1(-1(3 + 2x) + 5x * (3 + 2x)) = 0 14 + -1((3 * -1 + 2x * -1) + 5x * (3 + 2x)) = 0 14 + -1((-3 + -2x) + 5x * (3 + 2x)) = 0 14 + -1(-3 + -2x + (3 * 5x + 2x * 5x)) = 0 14 + -1(-3 + -2x + (15x + 10x2)) = 0 Combine like terms: -2x + 15x = 13x 14 + -1(-3 + 13x + 10x2) = 0 14 + (-3 * -1 + 13x * -1 + 10x2 * -1) = 0 14 + (3 + -13x + -10x2) = 0 Combine like terms: 14 + 3 = 17 17 + -13x + -10x2 = 0 Solving 17 + -13x + -10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -1.7 + 1.3x + x2 = 0.0 Move the constant term to the right: Add '1.7' to each side of the equation. -1.7 + 1.3x + 1.7 + x2 = 0.0 + 1.7 Reorder the terms: -1.7 + 1.7 + 1.3x + x2 = 0.0 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + 1.3x + x2 = 0.0 + 1.7 1.3x + x2 = 0.0 + 1.7 Combine like terms: 0.0 + 1.7 = 1.7 1.3x + x2 = 1.7 The x term is 1.3x. Take half its coefficient (0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. 1.3x + 0.4225 + x2 = 1.7 + 0.4225 Reorder the terms: 0.4225 + 1.3x + x2 = 1.7 + 0.4225 Combine like terms: 1.7 + 0.4225 = 2.1225 0.4225 + 1.3x + x2 = 2.1225 Factor a perfect square on the left side: (x + 0.65)(x + 0.65) = 2.1225 Calculate the square root of the right side: 1.456880228 Break this problem into two subproblems by setting (x + 0.65) equal to 1.456880228 and -1.456880228.Subproblem 1
x + 0.65 = 1.456880228 Simplifying x + 0.65 = 1.456880228 Reorder the terms: 0.65 + x = 1.456880228 Solving 0.65 + x = 1.456880228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + x = 1.456880228 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + x = 1.456880228 + -0.65 x = 1.456880228 + -0.65 Combine like terms: 1.456880228 + -0.65 = 0.806880228 x = 0.806880228 Simplifying x = 0.806880228Subproblem 2
x + 0.65 = -1.456880228 Simplifying x + 0.65 = -1.456880228 Reorder the terms: 0.65 + x = -1.456880228 Solving 0.65 + x = -1.456880228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + x = -1.456880228 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + x = -1.456880228 + -0.65 x = -1.456880228 + -0.65 Combine like terms: -1.456880228 + -0.65 = -2.106880228 x = -2.106880228 Simplifying x = -2.106880228Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.806880228, -2.106880228}
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