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Simplifying 7(3 + -1x) * 2x = -9 Reorder the terms for easier multiplication: 7 * 2x(3 + -1x) = -9 Multiply 7 * 2 14x(3 + -1x) = -9 (3 * 14x + -1x * 14x) = -9 (42x + -14x2) = -9 Solving 42x + -14x2 = -9 Solving for variable 'x'. Reorder the terms: 9 + 42x + -14x2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 42x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -0.6428571429 + -3x + x2 = 0 Move the constant term to the right: Add '0.6428571429' to each side of the equation. -0.6428571429 + -3x + 0.6428571429 + x2 = 0 + 0.6428571429 Reorder the terms: -0.6428571429 + 0.6428571429 + -3x + x2 = 0 + 0.6428571429 Combine like terms: -0.6428571429 + 0.6428571429 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + 0.6428571429 -3x + x2 = 0 + 0.6428571429 Combine like terms: 0 + 0.6428571429 = 0.6428571429 -3x + x2 = 0.6428571429 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 0.6428571429 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.6428571429 + 2.25 Combine like terms: 0.6428571429 + 2.25 = 2.8928571429 2.25 + -3x + x2 = 2.8928571429 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.8928571429 Calculate the square root of the right side: 1.700840129 Break this problem into two subproblems by setting (x + -1.5) equal to 1.700840129 and -1.700840129.Subproblem 1
x + -1.5 = 1.700840129 Simplifying x + -1.5 = 1.700840129 Reorder the terms: -1.5 + x = 1.700840129 Solving -1.5 + x = 1.700840129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.700840129 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.700840129 + 1.5 x = 1.700840129 + 1.5 Combine like terms: 1.700840129 + 1.5 = 3.200840129 x = 3.200840129 Simplifying x = 3.200840129Subproblem 2
x + -1.5 = -1.700840129 Simplifying x + -1.5 = -1.700840129 Reorder the terms: -1.5 + x = -1.700840129 Solving -1.5 + x = -1.700840129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.700840129 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.700840129 + 1.5 x = -1.700840129 + 1.5 Combine like terms: -1.700840129 + 1.5 = -0.200840129 x = -0.200840129 Simplifying x = -0.200840129Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.200840129, -0.200840129}
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