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Simplifying 0 = (21x)(21x) + -2x + -40 Remove parenthesis around (21x) 0 = 21x(21x) + -2x + -40 Remove parenthesis around (21x) 0 = 21x * 21x + -2x + -40 Reorder the terms for easier multiplication: 0 = 21 * 21x * x + -2x + -40 Multiply 21 * 21 0 = 441x * x + -2x + -40 Multiply x * x 0 = 441x2 + -2x + -40 Reorder the terms: 0 = -40 + -2x + 441x2 Solving 0 = -40 + -2x + 441x2 Solving for variable 'x'. Combine like terms: 0 + 40 = 40 40 + 2x + -441x2 = -40 + -2x + 441x2 + 40 + 2x + -441x2 Reorder the terms: 40 + 2x + -441x2 = -40 + 40 + -2x + 2x + 441x2 + -441x2 Combine like terms: -40 + 40 = 0 40 + 2x + -441x2 = 0 + -2x + 2x + 441x2 + -441x2 40 + 2x + -441x2 = -2x + 2x + 441x2 + -441x2 Combine like terms: -2x + 2x = 0 40 + 2x + -441x2 = 0 + 441x2 + -441x2 40 + 2x + -441x2 = 441x2 + -441x2 Combine like terms: 441x2 + -441x2 = 0 40 + 2x + -441x2 = 0 Begin completing the square. Divide all terms by -441 the coefficient of the squared term: Divide each side by '-441'. -0.09070294785 + -0.004535147392x + x2 = 0 Move the constant term to the right: Add '0.09070294785' to each side of the equation. -0.09070294785 + -0.004535147392x + 0.09070294785 + x2 = 0 + 0.09070294785 Reorder the terms: -0.09070294785 + 0.09070294785 + -0.004535147392x + x2 = 0 + 0.09070294785 Combine like terms: -0.09070294785 + 0.09070294785 = 0.00000000000 0.00000000000 + -0.004535147392x + x2 = 0 + 0.09070294785 -0.004535147392x + x2 = 0 + 0.09070294785 Combine like terms: 0 + 0.09070294785 = 0.09070294785 -0.004535147392x + x2 = 0.09070294785 The x term is -0.004535147392x. Take half its coefficient (-0.002267573696). Square it (0.000005141890467) and add it to both sides. Add '0.000005141890467' to each side of the equation. -0.004535147392x + 0.000005141890467 + x2 = 0.09070294785 + 0.000005141890467 Reorder the terms: 0.000005141890467 + -0.004535147392x + x2 = 0.09070294785 + 0.000005141890467 Combine like terms: 0.09070294785 + 0.000005141890467 = 0.090708089740467 0.000005141890467 + -0.004535147392x + x2 = 0.090708089740467 Factor a perfect square on the left side: (x + -0.002267573696)(x + -0.002267573696) = 0.090708089740467 Calculate the square root of the right side: 0.301177837 Break this problem into two subproblems by setting (x + -0.002267573696) equal to 0.301177837 and -0.301177837.Subproblem 1
x + -0.002267573696 = 0.301177837 Simplifying x + -0.002267573696 = 0.301177837 Reorder the terms: -0.002267573696 + x = 0.301177837 Solving -0.002267573696 + x = 0.301177837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.002267573696' to each side of the equation. -0.002267573696 + 0.002267573696 + x = 0.301177837 + 0.002267573696 Combine like terms: -0.002267573696 + 0.002267573696 = 0.000000000000 0.000000000000 + x = 0.301177837 + 0.002267573696 x = 0.301177837 + 0.002267573696 Combine like terms: 0.301177837 + 0.002267573696 = 0.303445410696 x = 0.303445410696 Simplifying x = 0.303445410696Subproblem 2
x + -0.002267573696 = -0.301177837 Simplifying x + -0.002267573696 = -0.301177837 Reorder the terms: -0.002267573696 + x = -0.301177837 Solving -0.002267573696 + x = -0.301177837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.002267573696' to each side of the equation. -0.002267573696 + 0.002267573696 + x = -0.301177837 + 0.002267573696 Combine like terms: -0.002267573696 + 0.002267573696 = 0.000000000000 0.000000000000 + x = -0.301177837 + 0.002267573696 x = -0.301177837 + 0.002267573696 Combine like terms: -0.301177837 + 0.002267573696 = -0.298910263304 x = -0.298910263304 Simplifying x = -0.298910263304Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.303445410696, -0.298910263304}
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