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Simplifying 5x2 + 24x + -15 = 0 Reorder the terms: -15 + 24x + 5x2 = 0 Solving -15 + 24x + 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 + 4.8x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 4.8x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 4.8x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4.8x + x2 = 0 + 3 4.8x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 4.8x + x2 = 3 The x term is 4.8x. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8x + 5.76 + x2 = 3 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = 3 + 5.76 Combine like terms: 3 + 5.76 = 8.76 5.76 + 4.8x + x2 = 8.76 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 8.76 Calculate the square root of the right side: 2.959729717 Break this problem into two subproblems by setting (x + 2.4) equal to 2.959729717 and -2.959729717.Subproblem 1
x + 2.4 = 2.959729717 Simplifying x + 2.4 = 2.959729717 Reorder the terms: 2.4 + x = 2.959729717 Solving 2.4 + x = 2.959729717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = 2.959729717 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 2.959729717 + -2.4 x = 2.959729717 + -2.4 Combine like terms: 2.959729717 + -2.4 = 0.559729717 x = 0.559729717 Simplifying x = 0.559729717Subproblem 2
x + 2.4 = -2.959729717 Simplifying x + 2.4 = -2.959729717 Reorder the terms: 2.4 + x = -2.959729717 Solving 2.4 + x = -2.959729717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = -2.959729717 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -2.959729717 + -2.4 x = -2.959729717 + -2.4 Combine like terms: -2.959729717 + -2.4 = -5.359729717 x = -5.359729717 Simplifying x = -5.359729717Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.559729717, -5.359729717}
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