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Simplifying x2 + 4x2 + 4x + -15 = 0 Reorder the terms: -15 + 4x + x2 + 4x2 = 0 Combine like terms: x2 + 4x2 = 5x2 -15 + 4x + 5x2 = 0 Solving -15 + 4x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + 0.8x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.8x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.8x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.8x + x2 = 0 + 3 0.8x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.8x + x2 = 3 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 3 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 3 + 0.16 Combine like terms: 3 + 0.16 = 3.16 0.16 + 0.8x + x2 = 3.16 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 3.16 Calculate the square root of the right side: 1.777638883 Break this problem into two subproblems by setting (x + 0.4) equal to 1.777638883 and -1.777638883.Subproblem 1
x + 0.4 = 1.777638883 Simplifying x + 0.4 = 1.777638883 Reorder the terms: 0.4 + x = 1.777638883 Solving 0.4 + x = 1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.777638883 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.777638883 + -0.4 x = 1.777638883 + -0.4 Combine like terms: 1.777638883 + -0.4 = 1.377638883 x = 1.377638883 Simplifying x = 1.377638883Subproblem 2
x + 0.4 = -1.777638883 Simplifying x + 0.4 = -1.777638883 Reorder the terms: 0.4 + x = -1.777638883 Solving 0.4 + x = -1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.777638883 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.777638883 + -0.4 x = -1.777638883 + -0.4 Combine like terms: -1.777638883 + -0.4 = -2.177638883 x = -2.177638883 Simplifying x = -2.177638883Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.377638883, -2.177638883}
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