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Simplifying 9x2 + 4x = 25 Reorder the terms: 4x + 9x2 = 25 Solving 4x + 9x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 4x + 9x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.777777778 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '2.777777778' to each side of the equation. -2.777777778 + 0.4444444444x + 2.777777778 + x2 = 0 + 2.777777778 Reorder the terms: -2.777777778 + 2.777777778 + 0.4444444444x + x2 = 0 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + 0.4444444444x + x2 = 0 + 2.777777778 0.4444444444x + x2 = 0 + 2.777777778 Combine like terms: 0 + 2.777777778 = 2.777777778 0.4444444444x + x2 = 2.777777778 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 2.777777778 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 2.777777778 + 0.04938271604 Combine like terms: 2.777777778 + 0.04938271604 = 2.82716049404 0.04938271604 + 0.4444444444x + x2 = 2.82716049404 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 2.82716049404 Calculate the square root of the right side: 1.681416217 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 1.681416217 and -1.681416217.Subproblem 1
x + 0.2222222222 = 1.681416217 Simplifying x + 0.2222222222 = 1.681416217 Reorder the terms: 0.2222222222 + x = 1.681416217 Solving 0.2222222222 + x = 1.681416217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 1.681416217 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 1.681416217 + -0.2222222222 x = 1.681416217 + -0.2222222222 Combine like terms: 1.681416217 + -0.2222222222 = 1.4591939948 x = 1.4591939948 Simplifying x = 1.4591939948Subproblem 2
x + 0.2222222222 = -1.681416217 Simplifying x + 0.2222222222 = -1.681416217 Reorder the terms: 0.2222222222 + x = -1.681416217 Solving 0.2222222222 + x = -1.681416217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -1.681416217 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -1.681416217 + -0.2222222222 x = -1.681416217 + -0.2222222222 Combine like terms: -1.681416217 + -0.2222222222 = -1.9036384392 x = -1.9036384392 Simplifying x = -1.9036384392Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4591939948, -1.9036384392}
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