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Simplifying -42x2 + -47x + 51 = 0 Reorder the terms: 51 + -47x + -42x2 = 0 Solving 51 + -47x + -42x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -42 the coefficient of the squared term: Divide each side by '-42'. -1.214285714 + 1.119047619x + x2 = 0 Move the constant term to the right: Add '1.214285714' to each side of the equation. -1.214285714 + 1.119047619x + 1.214285714 + x2 = 0 + 1.214285714 Reorder the terms: -1.214285714 + 1.214285714 + 1.119047619x + x2 = 0 + 1.214285714 Combine like terms: -1.214285714 + 1.214285714 = 0.000000000 0.000000000 + 1.119047619x + x2 = 0 + 1.214285714 1.119047619x + x2 = 0 + 1.214285714 Combine like terms: 0 + 1.214285714 = 1.214285714 1.119047619x + x2 = 1.214285714 The x term is 1.119047619x. Take half its coefficient (0.5595238095). Square it (0.3130668934) and add it to both sides. Add '0.3130668934' to each side of the equation. 1.119047619x + 0.3130668934 + x2 = 1.214285714 + 0.3130668934 Reorder the terms: 0.3130668934 + 1.119047619x + x2 = 1.214285714 + 0.3130668934 Combine like terms: 1.214285714 + 0.3130668934 = 1.5273526074 0.3130668934 + 1.119047619x + x2 = 1.5273526074 Factor a perfect square on the left side: (x + 0.5595238095)(x + 0.5595238095) = 1.5273526074 Calculate the square root of the right side: 1.235861079 Break this problem into two subproblems by setting (x + 0.5595238095) equal to 1.235861079 and -1.235861079.Subproblem 1
x + 0.5595238095 = 1.235861079 Simplifying x + 0.5595238095 = 1.235861079 Reorder the terms: 0.5595238095 + x = 1.235861079 Solving 0.5595238095 + x = 1.235861079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5595238095' to each side of the equation. 0.5595238095 + -0.5595238095 + x = 1.235861079 + -0.5595238095 Combine like terms: 0.5595238095 + -0.5595238095 = 0.0000000000 0.0000000000 + x = 1.235861079 + -0.5595238095 x = 1.235861079 + -0.5595238095 Combine like terms: 1.235861079 + -0.5595238095 = 0.6763372695 x = 0.6763372695 Simplifying x = 0.6763372695Subproblem 2
x + 0.5595238095 = -1.235861079 Simplifying x + 0.5595238095 = -1.235861079 Reorder the terms: 0.5595238095 + x = -1.235861079 Solving 0.5595238095 + x = -1.235861079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5595238095' to each side of the equation. 0.5595238095 + -0.5595238095 + x = -1.235861079 + -0.5595238095 Combine like terms: 0.5595238095 + -0.5595238095 = 0.0000000000 0.0000000000 + x = -1.235861079 + -0.5595238095 x = -1.235861079 + -0.5595238095 Combine like terms: -1.235861079 + -0.5595238095 = -1.7953848885 x = -1.7953848885 Simplifying x = -1.7953848885Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6763372695, -1.7953848885}
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