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Simplifying 4x(4x) = 5x + 10 Remove parenthesis around (4x) 4x * 4x = 5x + 10 Reorder the terms for easier multiplication: 4 * 4x * x = 5x + 10 Multiply 4 * 4 16x * x = 5x + 10 Multiply x * x 16x2 = 5x + 10 Reorder the terms: 16x2 = 10 + 5x Solving 16x2 = 10 + 5x Solving for variable 'x'. Reorder the terms: -10 + -5x + 16x2 = 10 + 5x + -10 + -5x Reorder the terms: -10 + -5x + 16x2 = 10 + -10 + 5x + -5x Combine like terms: 10 + -10 = 0 -10 + -5x + 16x2 = 0 + 5x + -5x -10 + -5x + 16x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -10 + -5x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.625 + -0.3125x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.3125x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.3125x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.3125x + x2 = 0 + 0.625 -0.3125x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.3125x + x2 = 0.625 The x term is -0.3125x. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125x + 0.0244140625 + x2 = 0.625 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125x + x2 = 0.625 + 0.0244140625 Combine like terms: 0.625 + 0.0244140625 = 0.6494140625 0.0244140625 + -0.3125x + x2 = 0.6494140625 Factor a perfect square on the left side: (x + -0.15625)(x + -0.15625) = 0.6494140625 Calculate the square root of the right side: 0.80586231 Break this problem into two subproblems by setting (x + -0.15625) equal to 0.80586231 and -0.80586231.Subproblem 1
x + -0.15625 = 0.80586231 Simplifying x + -0.15625 = 0.80586231 Reorder the terms: -0.15625 + x = 0.80586231 Solving -0.15625 + x = 0.80586231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + x = 0.80586231 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = 0.80586231 + 0.15625 x = 0.80586231 + 0.15625 Combine like terms: 0.80586231 + 0.15625 = 0.96211231 x = 0.96211231 Simplifying x = 0.96211231Subproblem 2
x + -0.15625 = -0.80586231 Simplifying x + -0.15625 = -0.80586231 Reorder the terms: -0.15625 + x = -0.80586231 Solving -0.15625 + x = -0.80586231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + x = -0.80586231 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = -0.80586231 + 0.15625 x = -0.80586231 + 0.15625 Combine like terms: -0.80586231 + 0.15625 = -0.64961231 x = -0.64961231 Simplifying x = -0.64961231Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.96211231, -0.64961231}
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