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Simplifying 15x2 = 3x + 7 Reorder the terms: 15x2 = 7 + 3x Solving 15x2 = 7 + 3x Solving for variable 'x'. Reorder the terms: -7 + -3x + 15x2 = 7 + 3x + -7 + -3x Reorder the terms: -7 + -3x + 15x2 = 7 + -7 + 3x + -3x Combine like terms: 7 + -7 = 0 -7 + -3x + 15x2 = 0 + 3x + -3x -7 + -3x + 15x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -7 + -3x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.4666666667 + -0.2x + x2 = 0 Move the constant term to the right: Add '0.4666666667' to each side of the equation. -0.4666666667 + -0.2x + 0.4666666667 + x2 = 0 + 0.4666666667 Reorder the terms: -0.4666666667 + 0.4666666667 + -0.2x + x2 = 0 + 0.4666666667 Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000 0.0000000000 + -0.2x + x2 = 0 + 0.4666666667 -0.2x + x2 = 0 + 0.4666666667 Combine like terms: 0 + 0.4666666667 = 0.4666666667 -0.2x + x2 = 0.4666666667 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 0.4666666667 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 0.4666666667 + 0.01 Combine like terms: 0.4666666667 + 0.01 = 0.4766666667 0.01 + -0.2x + x2 = 0.4766666667 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 0.4766666667 Calculate the square root of the right side: 0.690410506 Break this problem into two subproblems by setting (x + -0.1) equal to 0.690410506 and -0.690410506.Subproblem 1
x + -0.1 = 0.690410506 Simplifying x + -0.1 = 0.690410506 Reorder the terms: -0.1 + x = 0.690410506 Solving -0.1 + x = 0.690410506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 0.690410506 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.690410506 + 0.1 x = 0.690410506 + 0.1 Combine like terms: 0.690410506 + 0.1 = 0.790410506 x = 0.790410506 Simplifying x = 0.790410506Subproblem 2
x + -0.1 = -0.690410506 Simplifying x + -0.1 = -0.690410506 Reorder the terms: -0.1 + x = -0.690410506 Solving -0.1 + x = -0.690410506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -0.690410506 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -0.690410506 + 0.1 x = -0.690410506 + 0.1 Combine like terms: -0.690410506 + 0.1 = -0.590410506 x = -0.590410506 Simplifying x = -0.590410506Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.790410506, -0.590410506}
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