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Simplifying (6x + 4) * 10x = 90 Reorder the terms: (4 + 6x) * 10x = 90 Reorder the terms for easier multiplication: 10x(4 + 6x) = 90 (4 * 10x + 6x * 10x) = 90 (40x + 60x2) = 90 Solving 40x + 60x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 40x + 60x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 40x + 60x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-9 + 4x + 6x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-9 + 4x + 6x2)' equal to zero and attempt to solve: Simplifying -9 + 4x + 6x2 = 0 Solving -9 + 4x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.5 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 0.6666666667x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 0.6666666667x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 0.6666666667x + x2 = 0 + 1.5 0.6666666667x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 0.6666666667x + x2 = 1.5 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 1.5 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 1.5 + 0.1111111112 Combine like terms: 1.5 + 0.1111111112 = 1.6111111112 0.1111111112 + 0.6666666667x + x2 = 1.6111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 1.6111111112 Calculate the square root of the right side: 1.269295518 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 1.269295518 and -1.269295518.Subproblem 1
x + 0.3333333334 = 1.269295518 Simplifying x + 0.3333333334 = 1.269295518 Reorder the terms: 0.3333333334 + x = 1.269295518 Solving 0.3333333334 + x = 1.269295518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 1.269295518 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.269295518 + -0.3333333334 x = 1.269295518 + -0.3333333334 Combine like terms: 1.269295518 + -0.3333333334 = 0.9359621846 x = 0.9359621846 Simplifying x = 0.9359621846Subproblem 2
x + 0.3333333334 = -1.269295518 Simplifying x + 0.3333333334 = -1.269295518 Reorder the terms: 0.3333333334 + x = -1.269295518 Solving 0.3333333334 + x = -1.269295518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -1.269295518 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.269295518 + -0.3333333334 x = -1.269295518 + -0.3333333334 Combine like terms: -1.269295518 + -0.3333333334 = -1.6026288514 x = -1.6026288514 Simplifying x = -1.6026288514Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9359621846, -1.6026288514}Solution
x = {0.9359621846, -1.6026288514}
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