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Simplifying 0.3x + 24 * 5x * 0.2x + -15 = 0 Reorder the terms for easier multiplication: 0.3x + 24 * 5 * 0.2x * x + -15 = 0 Multiply 24 * 5 0.3x + 120 * 0.2x * x + -15 = 0 Multiply 120 * 0.2 0.3x + 24x * x + -15 = 0 Multiply x * x 0.3x + 24x2 + -15 = 0 Reorder the terms: -15 + 0.3x + 24x2 = 0 Solving -15 + 0.3x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.625 + 0.0125x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 0.0125x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 0.0125x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 0.0125x + x2 = 0 + 0.625 0.0125x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 0.0125x + x2 = 0.625 The x term is 0.0125x. Take half its coefficient (0.00625). Square it (0.0000390625) and add it to both sides. Add '0.0000390625' to each side of the equation. 0.0125x + 0.0000390625 + x2 = 0.625 + 0.0000390625 Reorder the terms: 0.0000390625 + 0.0125x + x2 = 0.625 + 0.0000390625 Combine like terms: 0.625 + 0.0000390625 = 0.6250390625 0.0000390625 + 0.0125x + x2 = 0.6250390625 Factor a perfect square on the left side: (x + 0.00625)(x + 0.00625) = 0.6250390625 Calculate the square root of the right side: 0.79059412 Break this problem into two subproblems by setting (x + 0.00625) equal to 0.79059412 and -0.79059412.Subproblem 1
x + 0.00625 = 0.79059412 Simplifying x + 0.00625 = 0.79059412 Reorder the terms: 0.00625 + x = 0.79059412 Solving 0.00625 + x = 0.79059412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00625' to each side of the equation. 0.00625 + -0.00625 + x = 0.79059412 + -0.00625 Combine like terms: 0.00625 + -0.00625 = 0.00000 0.00000 + x = 0.79059412 + -0.00625 x = 0.79059412 + -0.00625 Combine like terms: 0.79059412 + -0.00625 = 0.78434412 x = 0.78434412 Simplifying x = 0.78434412Subproblem 2
x + 0.00625 = -0.79059412 Simplifying x + 0.00625 = -0.79059412 Reorder the terms: 0.00625 + x = -0.79059412 Solving 0.00625 + x = -0.79059412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00625' to each side of the equation. 0.00625 + -0.00625 + x = -0.79059412 + -0.00625 Combine like terms: 0.00625 + -0.00625 = 0.00000 0.00000 + x = -0.79059412 + -0.00625 x = -0.79059412 + -0.00625 Combine like terms: -0.79059412 + -0.00625 = -0.79684412 x = -0.79684412 Simplifying x = -0.79684412Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.78434412, -0.79684412}
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