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Simplifying 15x2 + 7x = 6 Reorder the terms: 7x + 15x2 = 6 Solving 7x + 15x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 7x + 15x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 7x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.4 + 0.4666666667x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.4666666667x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.4666666667x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.4666666667x + x2 = 0 + 0.4 0.4666666667x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.4666666667x + x2 = 0.4 The x term is 0.4666666667x. Take half its coefficient (0.2333333334). Square it (0.05444444448) and add it to both sides. Add '0.05444444448' to each side of the equation. 0.4666666667x + 0.05444444448 + x2 = 0.4 + 0.05444444448 Reorder the terms: 0.05444444448 + 0.4666666667x + x2 = 0.4 + 0.05444444448 Combine like terms: 0.4 + 0.05444444448 = 0.45444444448 0.05444444448 + 0.4666666667x + x2 = 0.45444444448 Factor a perfect square on the left side: (x + 0.2333333334)(x + 0.2333333334) = 0.45444444448 Calculate the square root of the right side: 0.674124947 Break this problem into two subproblems by setting (x + 0.2333333334) equal to 0.674124947 and -0.674124947.Subproblem 1
x + 0.2333333334 = 0.674124947 Simplifying x + 0.2333333334 = 0.674124947 Reorder the terms: 0.2333333334 + x = 0.674124947 Solving 0.2333333334 + x = 0.674124947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2333333334' to each side of the equation. 0.2333333334 + -0.2333333334 + x = 0.674124947 + -0.2333333334 Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000 0.0000000000 + x = 0.674124947 + -0.2333333334 x = 0.674124947 + -0.2333333334 Combine like terms: 0.674124947 + -0.2333333334 = 0.4407916136 x = 0.4407916136 Simplifying x = 0.4407916136Subproblem 2
x + 0.2333333334 = -0.674124947 Simplifying x + 0.2333333334 = -0.674124947 Reorder the terms: 0.2333333334 + x = -0.674124947 Solving 0.2333333334 + x = -0.674124947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2333333334' to each side of the equation. 0.2333333334 + -0.2333333334 + x = -0.674124947 + -0.2333333334 Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000 0.0000000000 + x = -0.674124947 + -0.2333333334 x = -0.674124947 + -0.2333333334 Combine like terms: -0.674124947 + -0.2333333334 = -0.9074582804 x = -0.9074582804 Simplifying x = -0.9074582804Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4407916136, -0.9074582804}
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