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Simplifying 5X2 + 7X = 75 Reorder the terms: 7X + 5X2 = 75 Solving 7X + 5X2 = 75 Solving for variable 'X'. Reorder the terms: -75 + 7X + 5X2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 7X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -15 + 1.4X + X2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 1.4X + 15 + X2 = 0 + 15 Reorder the terms: -15 + 15 + 1.4X + X2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 1.4X + X2 = 0 + 15 1.4X + X2 = 0 + 15 Combine like terms: 0 + 15 = 15 1.4X + X2 = 15 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 = 15 + 0.49 Reorder the terms: 0.49 + 1.4X + X2 = 15 + 0.49 Combine like terms: 15 + 0.49 = 15.49 0.49 + 1.4X + X2 = 15.49 Factor a perfect square on the left side: (X + 0.7)(X + 0.7) = 15.49 Calculate the square root of the right side: 3.935733731 Break this problem into two subproblems by setting (X + 0.7) equal to 3.935733731 and -3.935733731.Subproblem 1
X + 0.7 = 3.935733731 Simplifying X + 0.7 = 3.935733731 Reorder the terms: 0.7 + X = 3.935733731 Solving 0.7 + X = 3.935733731 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 = 3.935733731 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + X = 3.935733731 + -0.7 X = 3.935733731 + -0.7 Combine like terms: 3.935733731 + -0.7 = 3.235733731 X = 3.235733731 Simplifying X = 3.235733731Subproblem 2
X + 0.7 = -3.935733731 Simplifying X + 0.7 = -3.935733731 Reorder the terms: 0.7 + X = -3.935733731 Solving 0.7 + X = -3.935733731 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 = -3.935733731 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + X = -3.935733731 + -0.7 X = -3.935733731 + -0.7 Combine like terms: -3.935733731 + -0.7 = -4.635733731 X = -4.635733731 Simplifying X = -4.635733731Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.235733731, -4.635733731}
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