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Simplifying 2x2 + -3x + -4(4x + 5) = 0 Reorder the terms: 2x2 + -3x + -4(5 + 4x) = 0 2x2 + -3x + (5 * -4 + 4x * -4) = 0 2x2 + -3x + (-20 + -16x) = 0 Reorder the terms: -20 + -3x + -16x + 2x2 = 0 Combine like terms: -3x + -16x = -19x -20 + -19x + 2x2 = 0 Solving -20 + -19x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10 + -9.5x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -9.5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -9.5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -9.5x + x2 = 0 + 10 -9.5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -9.5x + x2 = 10 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 10 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 10 + 22.5625 Combine like terms: 10 + 22.5625 = 32.5625 22.5625 + -9.5x + x2 = 32.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 32.5625 Calculate the square root of the right side: 5.706356105 Break this problem into two subproblems by setting (x + -4.75) equal to 5.706356105 and -5.706356105.Subproblem 1
x + -4.75 = 5.706356105 Simplifying x + -4.75 = 5.706356105 Reorder the terms: -4.75 + x = 5.706356105 Solving -4.75 + x = 5.706356105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 5.706356105 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 5.706356105 + 4.75 x = 5.706356105 + 4.75 Combine like terms: 5.706356105 + 4.75 = 10.456356105 x = 10.456356105 Simplifying x = 10.456356105Subproblem 2
x + -4.75 = -5.706356105 Simplifying x + -4.75 = -5.706356105 Reorder the terms: -4.75 + x = -5.706356105 Solving -4.75 + x = -5.706356105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -5.706356105 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -5.706356105 + 4.75 x = -5.706356105 + 4.75 Combine like terms: -5.706356105 + 4.75 = -0.956356105 x = -0.956356105 Simplifying x = -0.956356105Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.456356105, -0.956356105}
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