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Simplifying 4x(121x + 172) = -3x + -4 Reorder the terms: 4x(172 + 121x) = -3x + -4 (172 * 4x + 121x * 4x) = -3x + -4 (688x + 484x2) = -3x + -4 Reorder the terms: 688x + 484x2 = -4 + -3x Solving 688x + 484x2 = -4 + -3x Solving for variable 'x'. Reorder the terms: 4 + 688x + 3x + 484x2 = -4 + -3x + 4 + 3x Combine like terms: 688x + 3x = 691x 4 + 691x + 484x2 = -4 + -3x + 4 + 3x Reorder the terms: 4 + 691x + 484x2 = -4 + 4 + -3x + 3x Combine like terms: -4 + 4 = 0 4 + 691x + 484x2 = 0 + -3x + 3x 4 + 691x + 484x2 = -3x + 3x Combine like terms: -3x + 3x = 0 4 + 691x + 484x2 = 0 Begin completing the square. Divide all terms by 484 the coefficient of the squared term: Divide each side by '484'. 0.00826446281 + 1.42768595x + x2 = 0 Move the constant term to the right: Add '-0.00826446281' to each side of the equation. 0.00826446281 + 1.42768595x + -0.00826446281 + x2 = 0 + -0.00826446281 Reorder the terms: 0.00826446281 + -0.00826446281 + 1.42768595x + x2 = 0 + -0.00826446281 Combine like terms: 0.00826446281 + -0.00826446281 = 0.00000000000 0.00000000000 + 1.42768595x + x2 = 0 + -0.00826446281 1.42768595x + x2 = 0 + -0.00826446281 Combine like terms: 0 + -0.00826446281 = -0.00826446281 1.42768595x + x2 = -0.00826446281 The x term is 1.42768595x. Take half its coefficient (0.713842975). Square it (0.5095717930) and add it to both sides. Add '0.5095717930' to each side of the equation. 1.42768595x + 0.5095717930 + x2 = -0.00826446281 + 0.5095717930 Reorder the terms: 0.5095717930 + 1.42768595x + x2 = -0.00826446281 + 0.5095717930 Combine like terms: -0.00826446281 + 0.5095717930 = 0.50130733019 0.5095717930 + 1.42768595x + x2 = 0.50130733019 Factor a perfect square on the left side: (x + 0.713842975)(x + 0.713842975) = 0.50130733019 Calculate the square root of the right side: 0.7080306 Break this problem into two subproblems by setting (x + 0.713842975) equal to 0.7080306 and -0.7080306.Subproblem 1
x + 0.713842975 = 0.7080306 Simplifying x + 0.713842975 = 0.7080306 Reorder the terms: 0.713842975 + x = 0.7080306 Solving 0.713842975 + x = 0.7080306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.713842975' to each side of the equation. 0.713842975 + -0.713842975 + x = 0.7080306 + -0.713842975 Combine like terms: 0.713842975 + -0.713842975 = 0.000000000 0.000000000 + x = 0.7080306 + -0.713842975 x = 0.7080306 + -0.713842975 Combine like terms: 0.7080306 + -0.713842975 = -0.005812375 x = -0.005812375 Simplifying x = -0.005812375Subproblem 2
x + 0.713842975 = -0.7080306 Simplifying x + 0.713842975 = -0.7080306 Reorder the terms: 0.713842975 + x = -0.7080306 Solving 0.713842975 + x = -0.7080306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.713842975' to each side of the equation. 0.713842975 + -0.713842975 + x = -0.7080306 + -0.713842975 Combine like terms: 0.713842975 + -0.713842975 = 0.000000000 0.000000000 + x = -0.7080306 + -0.713842975 x = -0.7080306 + -0.713842975 Combine like terms: -0.7080306 + -0.713842975 = -1.421873575 x = -1.421873575 Simplifying x = -1.421873575Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.005812375, -1.421873575}
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