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Simplifying 15x2 + 3x = 4 Reorder the terms: 3x + 15x2 = 4 Solving 3x + 15x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 3x + 15x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 3x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.2666666667 + 0.2x + x2 = 0 Move the constant term to the right: Add '0.2666666667' to each side of the equation. -0.2666666667 + 0.2x + 0.2666666667 + x2 = 0 + 0.2666666667 Reorder the terms: -0.2666666667 + 0.2666666667 + 0.2x + x2 = 0 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + 0.2x + x2 = 0 + 0.2666666667 0.2x + x2 = 0 + 0.2666666667 Combine like terms: 0 + 0.2666666667 = 0.2666666667 0.2x + x2 = 0.2666666667 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 = 0.2666666667 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.2666666667 + 0.01 Combine like terms: 0.2666666667 + 0.01 = 0.2766666667 0.01 + 0.2x + x2 = 0.2766666667 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.2766666667 Calculate the square root of the right side: 0.525991128 Break this problem into two subproblems by setting (x + 0.1) equal to 0.525991128 and -0.525991128.Subproblem 1
x + 0.1 = 0.525991128 Simplifying x + 0.1 = 0.525991128 Reorder the terms: 0.1 + x = 0.525991128 Solving 0.1 + x = 0.525991128 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 = 0.525991128 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.525991128 + -0.1 x = 0.525991128 + -0.1 Combine like terms: 0.525991128 + -0.1 = 0.425991128 x = 0.425991128 Simplifying x = 0.425991128Subproblem 2
x + 0.1 = -0.525991128 Simplifying x + 0.1 = -0.525991128 Reorder the terms: 0.1 + x = -0.525991128 Solving 0.1 + x = -0.525991128 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 = -0.525991128 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.525991128 + -0.1 x = -0.525991128 + -0.1 Combine like terms: -0.525991128 + -0.1 = -0.625991128 x = -0.625991128 Simplifying x = -0.625991128Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.425991128, -0.625991128}
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