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Simplifying 5x2 + 7x + -2400 = 0 Reorder the terms: -2400 + 7x + 5x2 = 0 Solving -2400 + 7x + 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'. -480 + 1.4x + x2 = 0 Move the constant term to the right: Add '480' to each side of the equation. -480 + 1.4x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 1.4x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 1.4x + x2 = 0 + 480 1.4x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 1.4x + x2 = 480 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 480 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 480 + 0.49 Combine like terms: 480 + 0.49 = 480.49 0.49 + 1.4x + x2 = 480.49 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 480.49 Calculate the square root of the right side: 21.920082117 Break this problem into two subproblems by setting (x + 0.7) equal to 21.920082117 and -21.920082117.Subproblem 1
x + 0.7 = 21.920082117 Simplifying x + 0.7 = 21.920082117 Reorder the terms: 0.7 + x = 21.920082117 Solving 0.7 + x = 21.920082117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 21.920082117 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 21.920082117 + -0.7 x = 21.920082117 + -0.7 Combine like terms: 21.920082117 + -0.7 = 21.220082117 x = 21.220082117 Simplifying x = 21.220082117Subproblem 2
x + 0.7 = -21.920082117 Simplifying x + 0.7 = -21.920082117 Reorder the terms: 0.7 + x = -21.920082117 Solving 0.7 + x = -21.920082117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -21.920082117 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -21.920082117 + -0.7 x = -21.920082117 + -0.7 Combine like terms: -21.920082117 + -0.7 = -22.620082117 x = -22.620082117 Simplifying x = -22.620082117Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.220082117, -22.620082117}
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