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Simplifying x(10x + 3) = 75 Reorder the terms: x(3 + 10x) = 75 (3 * x + 10x * x) = 75 (3x + 10x2) = 75 Solving 3x + 10x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + 3x + 10x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -7.5 + 0.3x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 0.3x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 0.3x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 0.3x + x2 = 0 + 7.5 0.3x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 0.3x + x2 = 7.5 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 7.5 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 7.5 + 0.0225 Combine like terms: 7.5 + 0.0225 = 7.5225 0.0225 + 0.3x + x2 = 7.5225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 7.5225 Calculate the square root of the right side: 2.74271763 Break this problem into two subproblems by setting (x + 0.15) equal to 2.74271763 and -2.74271763.Subproblem 1
x + 0.15 = 2.74271763 Simplifying x + 0.15 = 2.74271763 Reorder the terms: 0.15 + x = 2.74271763 Solving 0.15 + x = 2.74271763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 2.74271763 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 2.74271763 + -0.15 x = 2.74271763 + -0.15 Combine like terms: 2.74271763 + -0.15 = 2.59271763 x = 2.59271763 Simplifying x = 2.59271763Subproblem 2
x + 0.15 = -2.74271763 Simplifying x + 0.15 = -2.74271763 Reorder the terms: 0.15 + x = -2.74271763 Solving 0.15 + x = -2.74271763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -2.74271763 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -2.74271763 + -0.15 x = -2.74271763 + -0.15 Combine like terms: -2.74271763 + -0.15 = -2.89271763 x = -2.89271763 Simplifying x = -2.89271763Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.59271763, -2.89271763}
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