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Simplifying 5x2 + 10x + -144 = 0 Reorder the terms: -144 + 10x + 5x2 = 0 Solving -144 + 10x + 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'. -28.8 + 2x + x2 = 0 Move the constant term to the right: Add '28.8' to each side of the equation. -28.8 + 2x + 28.8 + x2 = 0 + 28.8 Reorder the terms: -28.8 + 28.8 + 2x + x2 = 0 + 28.8 Combine like terms: -28.8 + 28.8 = 0.0 0.0 + 2x + x2 = 0 + 28.8 2x + x2 = 0 + 28.8 Combine like terms: 0 + 28.8 = 28.8 2x + x2 = 28.8 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 28.8 + 1 Reorder the terms: 1 + 2x + x2 = 28.8 + 1 Combine like terms: 28.8 + 1 = 29.8 1 + 2x + x2 = 29.8 Factor a perfect square on the left side: (x + 1)(x + 1) = 29.8 Calculate the square root of the right side: 5.458937626 Break this problem into two subproblems by setting (x + 1) equal to 5.458937626 and -5.458937626.Subproblem 1
x + 1 = 5.458937626 Simplifying x + 1 = 5.458937626 Reorder the terms: 1 + x = 5.458937626 Solving 1 + x = 5.458937626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 5.458937626 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.458937626 + -1 x = 5.458937626 + -1 Combine like terms: 5.458937626 + -1 = 4.458937626 x = 4.458937626 Simplifying x = 4.458937626Subproblem 2
x + 1 = -5.458937626 Simplifying x + 1 = -5.458937626 Reorder the terms: 1 + x = -5.458937626 Solving 1 + x = -5.458937626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -5.458937626 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.458937626 + -1 x = -5.458937626 + -1 Combine like terms: -5.458937626 + -1 = -6.458937626 x = -6.458937626 Simplifying x = -6.458937626Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.458937626, -6.458937626}
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