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Simplifying 4x2 + -28x + 49(2x + -7) = 0 Reorder the terms: 4x2 + -28x + 49(-7 + 2x) = 0 4x2 + -28x + (-7 * 49 + 2x * 49) = 0 4x2 + -28x + (-343 + 98x) = 0 Reorder the terms: -343 + -28x + 98x + 4x2 = 0 Combine like terms: -28x + 98x = 70x -343 + 70x + 4x2 = 0 Solving -343 + 70x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -85.75 + 17.5x + x2 = 0 Move the constant term to the right: Add '85.75' to each side of the equation. -85.75 + 17.5x + 85.75 + x2 = 0 + 85.75 Reorder the terms: -85.75 + 85.75 + 17.5x + x2 = 0 + 85.75 Combine like terms: -85.75 + 85.75 = 0.00 0.00 + 17.5x + x2 = 0 + 85.75 17.5x + x2 = 0 + 85.75 Combine like terms: 0 + 85.75 = 85.75 17.5x + x2 = 85.75 The x term is 17.5x. Take half its coefficient (8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. 17.5x + 76.5625 + x2 = 85.75 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 85.75 + 76.5625 Combine like terms: 85.75 + 76.5625 = 162.3125 76.5625 + 17.5x + x2 = 162.3125 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 162.3125 Calculate the square root of the right side: 12.740192306 Break this problem into two subproblems by setting (x + 8.75) equal to 12.740192306 and -12.740192306.Subproblem 1
x + 8.75 = 12.740192306 Simplifying x + 8.75 = 12.740192306 Reorder the terms: 8.75 + x = 12.740192306 Solving 8.75 + x = 12.740192306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = 12.740192306 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 12.740192306 + -8.75 x = 12.740192306 + -8.75 Combine like terms: 12.740192306 + -8.75 = 3.990192306 x = 3.990192306 Simplifying x = 3.990192306Subproblem 2
x + 8.75 = -12.740192306 Simplifying x + 8.75 = -12.740192306 Reorder the terms: 8.75 + x = -12.740192306 Solving 8.75 + x = -12.740192306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = -12.740192306 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -12.740192306 + -8.75 x = -12.740192306 + -8.75 Combine like terms: -12.740192306 + -8.75 = -21.490192306 x = -21.490192306 Simplifying x = -21.490192306Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.990192306, -21.490192306}
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