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Simplifying 6x + 5x(3x + -6) = 10 Reorder the terms: 6x + 5x(-6 + 3x) = 10 6x + (-6 * 5x + 3x * 5x) = 10 6x + (-30x + 15x2) = 10 Combine like terms: 6x + -30x = -24x -24x + 15x2 = 10 Solving -24x + 15x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -24x + 15x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -24x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.6666666667 + -1.6x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -1.6x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -1.6x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -1.6x + x2 = 0 + 0.6666666667 -1.6x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -1.6x + x2 = 0.6666666667 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 0.6666666667 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 0.6666666667 + 0.64 Combine like terms: 0.6666666667 + 0.64 = 1.3066666667 0.64 + -1.6x + x2 = 1.3066666667 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 1.3066666667 Calculate the square root of the right side: 1.143095213 Break this problem into two subproblems by setting (x + -0.8) equal to 1.143095213 and -1.143095213.Subproblem 1
x + -0.8 = 1.143095213 Simplifying x + -0.8 = 1.143095213 Reorder the terms: -0.8 + x = 1.143095213 Solving -0.8 + x = 1.143095213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 1.143095213 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.143095213 + 0.8 x = 1.143095213 + 0.8 Combine like terms: 1.143095213 + 0.8 = 1.943095213 x = 1.943095213 Simplifying x = 1.943095213Subproblem 2
x + -0.8 = -1.143095213 Simplifying x + -0.8 = -1.143095213 Reorder the terms: -0.8 + x = -1.143095213 Solving -0.8 + x = -1.143095213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -1.143095213 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.143095213 + 0.8 x = -1.143095213 + 0.8 Combine like terms: -1.143095213 + 0.8 = -0.343095213 x = -0.343095213 Simplifying x = -0.343095213Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.943095213, -0.343095213}
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