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Simplifying 7x2 + -3x = 90 Reorder the terms: -3x + 7x2 = 90 Solving -3x + 7x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -3x + 7x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -12.85714286 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '12.85714286' to each side of the equation. -12.85714286 + -0.4285714286x + 12.85714286 + x2 = 0 + 12.85714286 Reorder the terms: -12.85714286 + 12.85714286 + -0.4285714286x + x2 = 0 + 12.85714286 Combine like terms: -12.85714286 + 12.85714286 = 0.00000000 0.00000000 + -0.4285714286x + x2 = 0 + 12.85714286 -0.4285714286x + x2 = 0 + 12.85714286 Combine like terms: 0 + 12.85714286 = 12.85714286 -0.4285714286x + x2 = 12.85714286 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = 12.85714286 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 12.85714286 + 0.04591836735 Combine like terms: 12.85714286 + 0.04591836735 = 12.90306122735 0.04591836735 + -0.4285714286x + x2 = 12.90306122735 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 12.90306122735 Calculate the square root of the right side: 3.592083132 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 3.592083132 and -3.592083132.Subproblem 1
x + -0.2142857143 = 3.592083132 Simplifying x + -0.2142857143 = 3.592083132 Reorder the terms: -0.2142857143 + x = 3.592083132 Solving -0.2142857143 + x = 3.592083132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = 3.592083132 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 3.592083132 + 0.2142857143 x = 3.592083132 + 0.2142857143 Combine like terms: 3.592083132 + 0.2142857143 = 3.8063688463 x = 3.8063688463 Simplifying x = 3.8063688463Subproblem 2
x + -0.2142857143 = -3.592083132 Simplifying x + -0.2142857143 = -3.592083132 Reorder the terms: -0.2142857143 + x = -3.592083132 Solving -0.2142857143 + x = -3.592083132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = -3.592083132 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -3.592083132 + 0.2142857143 x = -3.592083132 + 0.2142857143 Combine like terms: -3.592083132 + 0.2142857143 = -3.3777974177 x = -3.3777974177 Simplifying x = -3.3777974177Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.8063688463, -3.3777974177}
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