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Simplifying 7x(3x + 5) + -8 = 0.5(8x + 20) + -7x + 5 Reorder the terms: 7x(5 + 3x) + -8 = 0.5(8x + 20) + -7x + 5 (5 * 7x + 3x * 7x) + -8 = 0.5(8x + 20) + -7x + 5 (35x + 21x2) + -8 = 0.5(8x + 20) + -7x + 5 Reorder the terms: -8 + 35x + 21x2 = 0.5(8x + 20) + -7x + 5 Reorder the terms: -8 + 35x + 21x2 = 0.5(20 + 8x) + -7x + 5 -8 + 35x + 21x2 = (20 * 0.5 + 8x * 0.5) + -7x + 5 -8 + 35x + 21x2 = (10 + 4x) + -7x + 5 Reorder the terms: -8 + 35x + 21x2 = 10 + 5 + 4x + -7x Combine like terms: 10 + 5 = 15 -8 + 35x + 21x2 = 15 + 4x + -7x Combine like terms: 4x + -7x = -3x -8 + 35x + 21x2 = 15 + -3x Solving -8 + 35x + 21x2 = 15 + -3x Solving for variable 'x'. Reorder the terms: -8 + -15 + 35x + 3x + 21x2 = 15 + -3x + -15 + 3x Combine like terms: -8 + -15 = -23 -23 + 35x + 3x + 21x2 = 15 + -3x + -15 + 3x Combine like terms: 35x + 3x = 38x -23 + 38x + 21x2 = 15 + -3x + -15 + 3x Reorder the terms: -23 + 38x + 21x2 = 15 + -15 + -3x + 3x Combine like terms: 15 + -15 = 0 -23 + 38x + 21x2 = 0 + -3x + 3x -23 + 38x + 21x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -23 + 38x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.095238095 + 1.80952381x + x2 = 0 Move the constant term to the right: Add '1.095238095' to each side of the equation. -1.095238095 + 1.80952381x + 1.095238095 + x2 = 0 + 1.095238095 Reorder the terms: -1.095238095 + 1.095238095 + 1.80952381x + x2 = 0 + 1.095238095 Combine like terms: -1.095238095 + 1.095238095 = 0.000000000 0.000000000 + 1.80952381x + x2 = 0 + 1.095238095 1.80952381x + x2 = 0 + 1.095238095 Combine like terms: 0 + 1.095238095 = 1.095238095 1.80952381x + x2 = 1.095238095 The x term is 1.80952381x. Take half its coefficient (0.904761905). Square it (0.8185941047) and add it to both sides. Add '0.8185941047' to each side of the equation. 1.80952381x + 0.8185941047 + x2 = 1.095238095 + 0.8185941047 Reorder the terms: 0.8185941047 + 1.80952381x + x2 = 1.095238095 + 0.8185941047 Combine like terms: 1.095238095 + 0.8185941047 = 1.9138321997 0.8185941047 + 1.80952381x + x2 = 1.9138321997 Factor a perfect square on the left side: (x + 0.904761905)(x + 0.904761905) = 1.9138321997 Calculate the square root of the right side: 1.383413243 Break this problem into two subproblems by setting (x + 0.904761905) equal to 1.383413243 and -1.383413243.Subproblem 1
x + 0.904761905 = 1.383413243 Simplifying x + 0.904761905 = 1.383413243 Reorder the terms: 0.904761905 + x = 1.383413243 Solving 0.904761905 + x = 1.383413243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.904761905' to each side of the equation. 0.904761905 + -0.904761905 + x = 1.383413243 + -0.904761905 Combine like terms: 0.904761905 + -0.904761905 = 0.000000000 0.000000000 + x = 1.383413243 + -0.904761905 x = 1.383413243 + -0.904761905 Combine like terms: 1.383413243 + -0.904761905 = 0.478651338 x = 0.478651338 Simplifying x = 0.478651338Subproblem 2
x + 0.904761905 = -1.383413243 Simplifying x + 0.904761905 = -1.383413243 Reorder the terms: 0.904761905 + x = -1.383413243 Solving 0.904761905 + x = -1.383413243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.904761905' to each side of the equation. 0.904761905 + -0.904761905 + x = -1.383413243 + -0.904761905 Combine like terms: 0.904761905 + -0.904761905 = 0.000000000 0.000000000 + x = -1.383413243 + -0.904761905 x = -1.383413243 + -0.904761905 Combine like terms: -1.383413243 + -0.904761905 = -2.288175148 x = -2.288175148 Simplifying x = -2.288175148Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.478651338, -2.288175148}
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