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Simplifying 25x2 + -144x + -16 = 0 Reorder the terms: -16 + -144x + 25x2 = 0 Solving -16 + -144x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.64 + -5.76x + x2 = 0 Move the constant term to the right: Add '0.64' to each side of the equation. -0.64 + -5.76x + 0.64 + x2 = 0 + 0.64 Reorder the terms: -0.64 + 0.64 + -5.76x + x2 = 0 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + -5.76x + x2 = 0 + 0.64 -5.76x + x2 = 0 + 0.64 Combine like terms: 0 + 0.64 = 0.64 -5.76x + x2 = 0.64 The x term is -5.76x. Take half its coefficient (-2.88). Square it (8.2944) and add it to both sides. Add '8.2944' to each side of the equation. -5.76x + 8.2944 + x2 = 0.64 + 8.2944 Reorder the terms: 8.2944 + -5.76x + x2 = 0.64 + 8.2944 Combine like terms: 0.64 + 8.2944 = 8.9344 8.2944 + -5.76x + x2 = 8.9344 Factor a perfect square on the left side: (x + -2.88)(x + -2.88) = 8.9344 Calculate the square root of the right side: 2.989046671 Break this problem into two subproblems by setting (x + -2.88) equal to 2.989046671 and -2.989046671.Subproblem 1
x + -2.88 = 2.989046671 Simplifying x + -2.88 = 2.989046671 Reorder the terms: -2.88 + x = 2.989046671 Solving -2.88 + x = 2.989046671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.88' to each side of the equation. -2.88 + 2.88 + x = 2.989046671 + 2.88 Combine like terms: -2.88 + 2.88 = 0.00 0.00 + x = 2.989046671 + 2.88 x = 2.989046671 + 2.88 Combine like terms: 2.989046671 + 2.88 = 5.869046671 x = 5.869046671 Simplifying x = 5.869046671Subproblem 2
x + -2.88 = -2.989046671 Simplifying x + -2.88 = -2.989046671 Reorder the terms: -2.88 + x = -2.989046671 Solving -2.88 + x = -2.989046671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.88' to each side of the equation. -2.88 + 2.88 + x = -2.989046671 + 2.88 Combine like terms: -2.88 + 2.88 = 0.00 0.00 + x = -2.989046671 + 2.88 x = -2.989046671 + 2.88 Combine like terms: -2.989046671 + 2.88 = -0.109046671 x = -0.109046671 Simplifying x = -0.109046671Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.869046671, -0.109046671}
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