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Simplifying 3x + 64(2x(3x)) = 100 Remove parenthesis around (3x) 3x + 64(2x * 3x) = 100 Reorder the terms for easier multiplication: 3x + 64(2 * 3x * x) = 100 Multiply 2 * 3 3x + 64(6x * x) = 100 Multiply x * x 3x + 64(6x2) = 100 Remove parenthesis around (6x2) 3x + 64 * 6x2 = 100 Multiply 64 * 6 3x + 384x2 = 100 Solving 3x + 384x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 3x + 384x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 3x + 384x2 = 0 Begin completing the square. Divide all terms by 384 the coefficient of the squared term: Divide each side by '384'. -0.2604166667 + 0.0078125x + x2 = 0 Move the constant term to the right: Add '0.2604166667' to each side of the equation. -0.2604166667 + 0.0078125x + 0.2604166667 + x2 = 0 + 0.2604166667 Reorder the terms: -0.2604166667 + 0.2604166667 + 0.0078125x + x2 = 0 + 0.2604166667 Combine like terms: -0.2604166667 + 0.2604166667 = 0.0000000000 0.0000000000 + 0.0078125x + x2 = 0 + 0.2604166667 0.0078125x + x2 = 0 + 0.2604166667 Combine like terms: 0 + 0.2604166667 = 0.2604166667 0.0078125x + x2 = 0.2604166667 The x term is 0.0078125x. Take half its coefficient (0.00390625). Square it (0.00001525878906) and add it to both sides. Add '0.00001525878906' to each side of the equation. 0.0078125x + 0.00001525878906 + x2 = 0.2604166667 + 0.00001525878906 Reorder the terms: 0.00001525878906 + 0.0078125x + x2 = 0.2604166667 + 0.00001525878906 Combine like terms: 0.2604166667 + 0.00001525878906 = 0.26043192548906 0.00001525878906 + 0.0078125x + x2 = 0.26043192548906 Factor a perfect square on the left side: (x + 0.00390625)(x + 0.00390625) = 0.26043192548906 Calculate the square root of the right side: 0.510325313 Break this problem into two subproblems by setting (x + 0.00390625) equal to 0.510325313 and -0.510325313.Subproblem 1
x + 0.00390625 = 0.510325313 Simplifying x + 0.00390625 = 0.510325313 Reorder the terms: 0.00390625 + x = 0.510325313 Solving 0.00390625 + x = 0.510325313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00390625' to each side of the equation. 0.00390625 + -0.00390625 + x = 0.510325313 + -0.00390625 Combine like terms: 0.00390625 + -0.00390625 = 0.00000000 0.00000000 + x = 0.510325313 + -0.00390625 x = 0.510325313 + -0.00390625 Combine like terms: 0.510325313 + -0.00390625 = 0.506419063 x = 0.506419063 Simplifying x = 0.506419063Subproblem 2
x + 0.00390625 = -0.510325313 Simplifying x + 0.00390625 = -0.510325313 Reorder the terms: 0.00390625 + x = -0.510325313 Solving 0.00390625 + x = -0.510325313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00390625' to each side of the equation. 0.00390625 + -0.00390625 + x = -0.510325313 + -0.00390625 Combine like terms: 0.00390625 + -0.00390625 = 0.00000000 0.00000000 + x = -0.510325313 + -0.00390625 x = -0.510325313 + -0.00390625 Combine like terms: -0.510325313 + -0.00390625 = -0.514231563 x = -0.514231563 Simplifying x = -0.514231563Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.506419063, -0.514231563}
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