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Simplifying 4x2 + 7 = 13x Reorder the terms: 7 + 4x2 = 13x Solving 7 + 4x2 = 13x Solving for variable 'x'. Reorder the terms: 7 + -13x + 4x2 = 13x + -13x Combine like terms: 13x + -13x = 0 7 + -13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -3.25x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -3.25x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -3.25x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -3.25x + x2 = 0 + -1.75 -3.25x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -3.25x + x2 = -1.75 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = -1.75 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = -1.75 + 2.640625 Combine like terms: -1.75 + 2.640625 = 0.890625 2.640625 + -3.25x + x2 = 0.890625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (x + -1.625) equal to 0.943729304 and -0.943729304.Subproblem 1
x + -1.625 = 0.943729304 Simplifying x + -1.625 = 0.943729304 Reorder the terms: -1.625 + x = 0.943729304 Solving -1.625 + x = 0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 0.943729304 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 0.943729304 + 1.625 x = 0.943729304 + 1.625 Combine like terms: 0.943729304 + 1.625 = 2.568729304 x = 2.568729304 Simplifying x = 2.568729304Subproblem 2
x + -1.625 = -0.943729304 Simplifying x + -1.625 = -0.943729304 Reorder the terms: -1.625 + x = -0.943729304 Solving -1.625 + x = -0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -0.943729304 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -0.943729304 + 1.625 x = -0.943729304 + 1.625 Combine like terms: -0.943729304 + 1.625 = 0.681270696 x = 0.681270696 Simplifying x = 0.681270696Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.568729304, 0.681270696}
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