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Simplifying 4x(4x) = 13x + 35 Remove parenthesis around (4x) 4x * 4x = 13x + 35 Reorder the terms for easier multiplication: 4 * 4x * x = 13x + 35 Multiply 4 * 4 16x * x = 13x + 35 Multiply x * x 16x2 = 13x + 35 Reorder the terms: 16x2 = 35 + 13x Solving 16x2 = 35 + 13x Solving for variable 'x'. Reorder the terms: -35 + -13x + 16x2 = 35 + 13x + -35 + -13x Reorder the terms: -35 + -13x + 16x2 = 35 + -35 + 13x + -13x Combine like terms: 35 + -35 = 0 -35 + -13x + 16x2 = 0 + 13x + -13x -35 + -13x + 16x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -35 + -13x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.1875 + -0.8125x + x2 = 0 Move the constant term to the right: Add '2.1875' to each side of the equation. -2.1875 + -0.8125x + 2.1875 + x2 = 0 + 2.1875 Reorder the terms: -2.1875 + 2.1875 + -0.8125x + x2 = 0 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + -0.8125x + x2 = 0 + 2.1875 -0.8125x + x2 = 0 + 2.1875 Combine like terms: 0 + 2.1875 = 2.1875 -0.8125x + x2 = 2.1875 The x term is -0.8125x. Take half its coefficient (-0.40625). Square it (0.1650390625) and add it to both sides. Add '0.1650390625' to each side of the equation. -0.8125x + 0.1650390625 + x2 = 2.1875 + 0.1650390625 Reorder the terms: 0.1650390625 + -0.8125x + x2 = 2.1875 + 0.1650390625 Combine like terms: 2.1875 + 0.1650390625 = 2.3525390625 0.1650390625 + -0.8125x + x2 = 2.3525390625 Factor a perfect square on the left side: (x + -0.40625)(x + -0.40625) = 2.3525390625 Calculate the square root of the right side: 1.533798899 Break this problem into two subproblems by setting (x + -0.40625) equal to 1.533798899 and -1.533798899.Subproblem 1
x + -0.40625 = 1.533798899 Simplifying x + -0.40625 = 1.533798899 Reorder the terms: -0.40625 + x = 1.533798899 Solving -0.40625 + x = 1.533798899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + x = 1.533798899 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + x = 1.533798899 + 0.40625 x = 1.533798899 + 0.40625 Combine like terms: 1.533798899 + 0.40625 = 1.940048899 x = 1.940048899 Simplifying x = 1.940048899Subproblem 2
x + -0.40625 = -1.533798899 Simplifying x + -0.40625 = -1.533798899 Reorder the terms: -0.40625 + x = -1.533798899 Solving -0.40625 + x = -1.533798899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + x = -1.533798899 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + x = -1.533798899 + 0.40625 x = -1.533798899 + 0.40625 Combine like terms: -1.533798899 + 0.40625 = -1.127548899 x = -1.127548899 Simplifying x = -1.127548899Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.940048899, -1.127548899}
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