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Simplifying 6x(x + -4) + -16x2 + -1(9x + -1) = 0 Reorder the terms: 6x(-4 + x) + -16x2 + -1(9x + -1) = 0 (-4 * 6x + x * 6x) + -16x2 + -1(9x + -1) = 0 (-24x + 6x2) + -16x2 + -1(9x + -1) = 0 Reorder the terms: -24x + 6x2 + -16x2 + -1(-1 + 9x) = 0 -24x + 6x2 + -16x2 + (-1 * -1 + 9x * -1) = 0 -24x + 6x2 + -16x2 + (1 + -9x) = 0 Reorder the terms: 1 + -24x + -9x + 6x2 + -16x2 = 0 Combine like terms: -24x + -9x = -33x 1 + -33x + 6x2 + -16x2 = 0 Combine like terms: 6x2 + -16x2 = -10x2 1 + -33x + -10x2 = 0 Solving 1 + -33x + -10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.1 + 3.3x + x2 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 3.3x + 0.1 + x2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + 3.3x + x2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 3.3x + x2 = 0.0 + 0.1 3.3x + x2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 3.3x + x2 = 0.1 The x term is 3.3x. Take half its coefficient (1.65). Square it (2.7225) and add it to both sides. Add '2.7225' to each side of the equation. 3.3x + 2.7225 + x2 = 0.1 + 2.7225 Reorder the terms: 2.7225 + 3.3x + x2 = 0.1 + 2.7225 Combine like terms: 0.1 + 2.7225 = 2.8225 2.7225 + 3.3x + x2 = 2.8225 Factor a perfect square on the left side: (x + 1.65)(x + 1.65) = 2.8225 Calculate the square root of the right side: 1.680029762 Break this problem into two subproblems by setting (x + 1.65) equal to 1.680029762 and -1.680029762.Subproblem 1
x + 1.65 = 1.680029762 Simplifying x + 1.65 = 1.680029762 Reorder the terms: 1.65 + x = 1.680029762 Solving 1.65 + x = 1.680029762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.65' to each side of the equation. 1.65 + -1.65 + x = 1.680029762 + -1.65 Combine like terms: 1.65 + -1.65 = 0.00 0.00 + x = 1.680029762 + -1.65 x = 1.680029762 + -1.65 Combine like terms: 1.680029762 + -1.65 = 0.030029762 x = 0.030029762 Simplifying x = 0.030029762Subproblem 2
x + 1.65 = -1.680029762 Simplifying x + 1.65 = -1.680029762 Reorder the terms: 1.65 + x = -1.680029762 Solving 1.65 + x = -1.680029762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.65' to each side of the equation. 1.65 + -1.65 + x = -1.680029762 + -1.65 Combine like terms: 1.65 + -1.65 = 0.00 0.00 + x = -1.680029762 + -1.65 x = -1.680029762 + -1.65 Combine like terms: -1.680029762 + -1.65 = -3.330029762 x = -3.330029762 Simplifying x = -3.330029762Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.030029762, -3.330029762}
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